Download or read book A Perturbation Approach to Continuous Time Portfolio Selection written by Dietmar Leisen and published by . This book was released on 2016 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies portfolio selection in continuous-time models with stochastic investment opportunities. We consider asset allocation problems where preferences are specified as power utility derived from terminal wealth as well as consumption-savings problems with recursive utility Epstein-Zin preferences. The paper approximates the associated dynamic programming problem by perturbing the coefficients of the stochastic dynamics. We represent the Hamilton-Jacobi-Bellman equation as a series of partial differential equations that can be solved iteratively in closed-form through computer algebra software, at any desired accuracy.

Download or read book Optimal Portfolios written by Ralf Korn and published by World Scientific. This book was released on 1997 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of the book is the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. It begins by presenting the complete Black-Scholes type model and then moves on to incomplete models and models including constraints and transaction costs. The models and methods presented will include the stochastic control method of Merton, the martingale method of Cox-Huang and Karatzas et al., the log optimal method of Cover and Jamshidian, the value-preserving model of Hellwig etc.

Download or read book Continuous Time Markov Chains and Applications written by G. George Yin and published by Springer Science & Business Media. This book was released on 2012-11-14 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted to applications in controlled dynamic systems, production planning, and numerical methods for controlled Markovian systems with large-scale and complex structures in the real-world problems. This second edition has been updated throughout and includes two new chapters on asymptotic expansions of solutions for backward equations and hybrid LQG problems. The chapters on analytic and probabilistic properties of two-time-scale Markov chains have been almost completely rewritten and the notation has been streamlined and simplified. This book is written for applied mathematicians, engineers, operations researchers, and applied scientists. Selected material from the book can also be used for a one semester advanced graduate-level course in applied probability and stochastic processes.

Download or read book Continuous Time Portfolio Selection written by Se Yung Bae and published by . This book was released on 2020 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article we provide a short survey on continuous-time portfolio selection. We explain the pioneering contribution of Merton and the use of dynamic programming. Then, we discuss Bismut's application of the Pontryagin maximum principle to portfolio selection and the dual martingale approach. We also explain two models with potential applicability to practice: life-cycle models with explicit consideration of retirement and models with protection against decline in spending power.

Download or read book Portfolio Choice Problems written by Nicolas Chapados and published by Springer Science & Business Media. This book was released on 2011-07-12 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief offers a broad, yet concise, coverage of portfolio choice, containing both application-oriented and academic results, along with abundant pointers to the literature for further study. It cuts through many strands of the subject, presenting not only the classical results from financial economics but also approaches originating from information theory, machine learning and operations research. This compact treatment of the topic will be valuable to students entering the field, as well as practitioners looking for a broad coverage of the topic.

Download or read book Mean Variance Portfolio Management written by Kwok-Chuen Wong and published by Open Dissertation Press. This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Mean Variance Portfolio Management: Time Consistent Approach" by Kwok-chuen, Wong, 黃國全, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In this thesis, two problems of time consistent mean-variance portfolio selection have been studied: mean-variance asset-liability management with regime switchings and mean-variance optimization with state-dependent risk aversion under short-selling prohibition. Due to the non-linear expectation term in the mean-variance utility, the usual Tower Property fails to hold, and the corresponding optimal portfolio selection problem becomes time-inconsistent in the sense that it does not admit the Bellman Optimality Principle. Because of this, in this thesis, time-consistent equilibrium solution of two mean-variance optimization problems is established via a game theoretic approach. In the first part of this thesis, the time consistent solution of the mean-variance asset-liability management is sought for. By using the extended Hamilton-Jacobi- Bellman equation for equilibrium solution, equilibrium feedback control of this MVALM and the corresponding equilibrium value function can be obtained. The equilibrium control is found to be affine in liability. Hence, the time consistent equilibrium control of this problem is state dependent in the sense that it depends on the uncontrollable liability process, which is in substantial contrast with the time consistent solution of the simple classical mean-variance problem in Bjork and Murgoci (2010), in which it was independent of the state. In the second part of this thesis, the time consistent equilibrium strategies for the mean-variance portfolio selection with state dependent risk aversion under short-selling prohibition is studied in both a discrete and a continuous time set- tings. The motivation that urges us to study this problem is the recent work in Bjork et al. (2012) that considered the mean-variance problem with state dependent risk aversion in the sense that the risk aversion is inversely proportional to the current wealth. There is no short-selling restriction in their problem and the corresponding time consistent control was shown to be linear in wealth. However, we discovered that the counterpart of their continuous time equilibrium control in the discrete time framework behaves unsatisfactory, in the sense that the corresponding "optimal" wealth process can take negative values. This negativity in wealth will change the investor into a risk seeker which results in an unbounded value function that is economically unsound. Therefore, the discretized version of the problem in Bjork et al. (2012) might yield solutions with bankruptcy possibility. Furthermore, such "bankruptcy" solution can converge to the solution in continuous counterpart as Bjork et al. (2012). This means that the negative risk aversion drawback could appear in implementing the solution in Bjork et al. (2012) discretely in practice. This drawback urges us to prohibit short-selling in order to eliminate the chance of getting non-positive wealth. Using backward induction, the equilibrium control in discrete time setting is explicit solvable and is shown to be linear in wealth. An application of the extended Hamilton-Jacobi-Bellman equation leads us to conclude that the continuous time equilibrium control is also linear in wealth. Also, the investment to wealth ratio would satisfy an integral equation which is uniquely solvable. The discrete time equilibrium controls are shown to converge to that in continuous time setting. DOI: 10.5353/th_b5153743 S

Download or read book Discrete Time Markov Chains written by George Yin and published by Springer Science & Business Media. This book was released on 2005 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on discrete-time-scale Markov chains, the contents of this book are an outgrowth of some of the authors' recent research. The motivation stems from existing and emerging applications in optimization and control of complex hybrid Markovian systems in manufacturing, wireless communication, and financial engineering. Much effort in this book is devoted to designing system models arising from these applications, analyzing them via analytic and probabilistic techniques, and developing feasible computational algorithms so as to reduce the inherent complexity. This book presents results including asymptotic expansions of probability vectors, structural properties of occupation measures, exponential bounds, aggregation and decomposition and associated limit processes, and interface of discrete-time and continuous-time systems. One of the salient features is that it contains a diverse range of applications on filtering, estimation, control, optimization, and Markov decision processes, and financial engineering. This book will be an important reference for researchers in the areas of applied probability, control theory, operations research, as well as for practitioners who use optimization techniques. Part of the book can also be used in a graduate course of applied probability, stochastic processes, and applications.

Download or read book Modeling Stochastic Control Optimization and Applications written by George Yin and published by Springer. This book was released on 2019-07-16 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

Download or read book Image and Graphics Technologies and Applications written by Yongtian Wang and published by Springer Nature. This book was released on 2022-07-21 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th Chinese Conference on Image and Graphics Technologies and Applications, IGTA 2022, held in Beijing, China, during April 23–24, 2022. The 25 full papers included in this book were carefully reviewed and selected from 77 submissions. They were organized in topical sections as follows: image processing and enhancement techniques; machine vision and 3D reconstruction; image/Video big data analysis and understanding; computer graphics; visualization and visual analysis; applications of image and graphics.

Download or read book Portfolio Selection in Continuous Time written by Constantin Alexandru Filitti and published by . This book was released on 2004 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Penalty Methods for Continuous Time Portfolio Selection with Proportional Transaction Costs written by Min Dai and published by . This book was released on 2008 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We are concerned with numerical solutions for the continuous-time portfolio selection with proportional transaction costs which is described as a singular stochastic control problem. The associated value function is governed by a variational inequality with gradient constraints. We propose a penalty method to deal with the gradient constraints and employ the finite difference discretization. Convergence analysis is presented. We also show that the standard penalty method can be applied in the case of single risky asset where the problem can be reduced to a standard variational inequality. Numerical results are given to demonstrate the efficiency of the methods and to examine the behaviors of the optimal trading strategy.

Download or read book Dynamic Portfolio Selection and Risk Return Trade Off with Respect to Stock Price Jumps in Continuous Time written by Bernhard Nietert and published by . This book was released on 1997 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intertemporal continuous time portfolio selection models are rather easy to implement -they only need means and variances/covariances as input (and no higher moments). Moreover, they are able to gain closed form portfolio strategies and, as a by-product, compact pricing equations e.g. the continuous time CAPM. - However, both the tracta- bility and the theoretical content of continuous time models are closely connected with the stock price process assumed. Therefore, we introduce stock price jumps to get a more realistic representation of stock price movements. But optimization under jump risks calls for an completely new portfolio strategy. It does not work as simple as adjusting mean and standard deviation of the price process to jumps and use the old portfolio rules of the diffusion case. Instead, we have to explicitly integrate jump risks into portfolio planning via hedge terms. These hedge terms also enter pricing equations and hence, make both forms of jumps - firm-specific and market jumps - to contain systematic risk. Thus, we refute an opinion especially widespread in option pricing literature, e.g. Merton (1976), about the unsystematic character of firm-specific jump risks.

Download or read book Continuous Time Portfolio Selection Under Conditional Capital at Risk written by Gordana Dmitrasinovic-Vidovic and published by . This book was released on 2004 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimal Portfolio Selection with Fixed Transaction Costs in the Presence of Jumps and Random Drift written by Ajay Subramanian Aiyer and published by . This book was released on 1996 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applications of Stochastic Control to Portfolio Selection Problems written by Hongcan Lin and published by . This book was released on 2018 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Portfolio selection is an important problem both in academia and in practice. Due to its significance, it has received great attention and facilitated a large amount of research. This thesis is devoted to structuring optimal portfolios using different criteria. Participating contracts are popular insurance policies, in which the payoff to a policyholder is linked to the performance of a portfolio managed by the insurer. In Chapter 2, we consider the portfolio selection problem of an insurer that offers participating contracts and has an S-shaped utility function. Applying the martingale approach, closed-form solutions are obtained. The resulting optimal strategies are compared with two portfolio insurance hedging strategies, e.g. Constant Proportion Portfolio Insurance strategy and Option Based Portfolio Insurance strategy. We also study numerical solutions of the portfolio selection problem with constraints on the portfolio weights. In Chapter 3, we consider the portfolio selection problem of maximizing a performance measure in a continuous-time diffusion model. The performance measure is the ratio of the overperformance to the underperformance of a portfolio relative to a benchmark. Following a strategy from fractional programming, we analyze the problem by solving a family of related problems, where the objective functions are the numerator of the original problem minus the denominator multiplied by a penalty parameter. These auxiliary problems can be solved using the martingale method for stochastic control. The existence of a solution is discussed in a general setting and explicit solutions are derived when both the reward and the penalty functions are power functions. In Chapter 4, we consider the mean-risk portfolio selection problem of optimizing the expectile risk measure in a continuous-time diffusion model. Due to the lack of an explicit form for expectiles and the close relationship with the Omega measure, we propose an alternative optimization problem with the Omega measure as an objective and show the equivalence between the two problems. After showing the solution for the mean-expectile problem is not attainable but the value function is finite, we modify the problem with an upper bound constraint imposed on the terminal wealth and obtain the solution via the Lagrangian duality method and pointwise optimization technique. The global expectile minimizing portfolio and efficient frontier are also considered in our analysis. In Chapter 5, we consider the utility-based portfolio selection problem in a continuous-time setting. We assume the market price of risk depends on a stochastic factor that satisfies an affine-form, square-root, Markovian model. This financial market framework includes the classical geometric Brownian motion, the constant elasticity of variance (CEV) model and the Heston's model as special cases. Adopting the Backward Stochastic Differential Equation (BSDE) approach, we obtain the closed-form solutions for power, logarithm, or exponential utility functions, respectively. Concluding remarks and several potential topics for further research are presented in Chapter 6.

Download or read book Time Consistent Mean Variance Portfolio Selection with Only Risky Assets written by Chi Seng Pun and published by . This book was released on 2018 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-consistency and optimal diversification (minimum-variance) criteria are popular in the dynamic portfolio construction in practice. This paper is devoted to the exact analytic solution of the time-consistent mean-variance portfolio selection with assets that can be all risky in a continuous-time economy, of which the time-consistent global minimum-variance portfolio is a special case. Our solution generalizes the studies with a risk-free asset in the sense that one of the risky assets can be set as risk-free. By applying the extended dynamic programming, we manage to derive the exact analytic solution of the time-consistent mean-variance strategy with risky assets via the solution of the Abel differential equation. To stabilize the solution, we derive an analytical expansion for the Abel differential equation with any desired accuracy. In addition, we derive the statistical properties of the optimal strategy and prove a separation theorem. Moreover, we establish the links of time-consistent strategy with pre-commitment and myopic strategies and investigate the curse of dimensionality on the time-consistent strategies. We show that under the low-dimensional setting, the intertemporal hedging demands are significant; however, under the high-dimensional setting, the time-consistent strategies are approximately equivalent to myopic strategies, in the presence of estimation risk. Empirical studies are conducted to illustrate and verify our results.

Download or read book Paris Princeton Lectures on Mathematical Finance 2004 written by René Carmona and published by Springer. This book was released on 2007-08-10 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume in the Paris-Princeton Lectures in Financial Mathematics, which publishes, on an annual basis, cutting-edge research in self-contained, expository articles from outstanding specialists, both established and upcoming. Coverage includes articles by René Carmona, Ivar Ekeland/Erik Taflin, Arturo Kohatsu-Higa, Pierre-Louis Lions/Jean-Michel Lasry, and Huyên Pham.