Download or read book Capital Allocation La Aumann Shapley for Non Differentiable Risk Measures written by Francesca Centrone and published by . This book was released on 2017 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a family of Capital allocation rules (C.A.R) based on the dual representation for risk measures and inspired to the Aumann-Shapley allocation principle. These rules extend the one of Denault and Kalkbrener (for coherent risk measures) and the one of Tsanakas (convex case), to the case of non Gateaux differentiable risk measures. We also study their properties and discuss their suitability in the quasiconvex context.
Download or read book Mathematical Finance written by Emanuela Rosazza Gianin and published by Springer Nature. This book was released on 2023-04-18 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is conceived as a guide to solve exercises in Mathematical Finance and a complement to theoretical lectures. The potential audience consists of students in Applied Mathematics, Engineering and Economics, attending courses in Mathematical Finance. The most important subjects covered by this textbook are Pricing and Hedging of different classes of financial derivatives (European, American Exotic options, Fixed Income derivatives) in the most popular modeling frameworks, both in discrete and continuous time setting, like the Binomial and the Black-Scholes models. A Chapter on static portfolio optimization, one on pricing for more advanced models and one on Risk Measures complete the overview on the main issues presented in classical courses on Mathematical Finance. About one hundred exercises are proposed, and a large amount of them provides a detailed solution, while a few are left as an exercise to the reader. Every chapter includes a brief resume of the main theoretical results to apply. This textbook is the result of several years of teaching experience of both the authors.
Download or read book To Split or Not to Split written by Andreas Tsanakas and published by . This book was released on 2014 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex risk measures were introduced by Deprez and Gerber (1985). Here the problem of allocating risk capital to subportfolios is addressed, when aggregate capital is calculated by a convex risk measure. The Aumann-Shapley value is proposed as an appropriate allocation mechanism. Distortion-exponential measures are discussed extensively and explicit capital allocation formulas are obtained for the case that the risk measure belongs to this family. Finally the implications of capital allocation with a convex risk measure for the stability of portfolios are discussed.
Download or read book Dynamic Capital Allocation With Distortion Risk Measures written by Andreas Tsanakas and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tsanakas and Barnett (2002) employed concepts from cooperative game theory (Aumann and Shapley, 1974) for the allocation of risk capital to portfolios of pooled liabilities, when distortion risk measures (Wang et al., 1997) are used. In this paper we generalise previously obtained results in three directions. Firstly, we allow for the presence of non-linear portfolios. Secondly, based on the concept of correlation order (Dhaene and Goovaerts, 1996) we proceed with discussing the links between dependence structures, capital allocation and pricing, as well as dropping a restrictive assumption on the continuity of probability distributions. Finally, we generalise the capital allocation methodology to a dynamic setting and conclude with a numerical example.
Download or read book Capital Allocation for Portfolios with Non Linear Risk Aggregation written by Tim J. Boonen and published by . This book was released on 2016 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: Existing risk capital allocation methods, such as the Euler rule, work under the explicit assumption that portfolios are formed as linear combinations of random loss/profit variables, with the firm being able to choose the portfolio weights. This assumption is unrealistic in an insurance context, where arbitrary scaling of risks is generally not possible. Here, we model risks as being partially generated by L'evy processes, capturing the non-linear aggregation of insurance risk. The model leads to non-homogeneous fuzzy games, for which the Euler rule is not applicable. For such games, we seek capital allocations that are in the core, that is, do not provide incentives for splitting portfolios. We show that the Euler rule of an auxiliary linearized game (non-uniquely) satisfies the core property and, thus, provides a plausible and easily implemented capital allocation. In contrast, the Aumann-Shapley allocation, does not generally belong to the core. For the non-homogeneous fuzzy games studied, Tasche's (1999) criterion of suitability for performance measurement is adapted and it is shown that the proposed allocation method gives appropriate signals for improving the portfolio underwriting profit.
Download or read book Economic Capital Allocation Using Risk Measures and Game Theory written by Luca Festini and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Economic Capital Allocation Derived from Risk Measures written by M. J. Goovaerts and published by . This book was released on 2002 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Risk Capital Allocation by Coherent Risk Measures Based on One side Moments written by Tom Fischer and published by . This book was released on 2002 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differentiability of BSVIEs and Dynamic Capital Allocations written by Eduard Kromer and published by . This book was released on 2015 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Capital allocations have been studied in conjunction with static risk measures in various papers. The dynamic case has been studied only in a discrete-time setting. We address the problem of allocating risk capital to subportfolios in a continuous-time dynamic context. For this purpose we introduce a classical differentiability result for backward stochastic Volterra integral equations and apply this result to derive continuous-time dynamic capital allocations. Moreover, we study a dynamic capital allocation principle that is based on backward stochastic differential equations and derive the dynamic gradient allocation for the dynamic entropic risk measure.
Download or read book A Generalization of the Aumann Shapley Value for Risk Allocation Problems written by Tim Boonen and published by . This book was released on 2012 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Risk Measures and Capital Allocation written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This research first gives a review of risk measures and risk capital allocation, along with the important property of coherency, and the relationships between different coherent risk measures. Secondly, relative accuracy measures are used as model-based criteria to study whether or not bias adjustment by various bootstrap techniques could improve estimates of the expected shortfall (ES) as a risk measure. Thirdly, different tests for backtesting Value-at-Risk (VaR) and ES are investigated as data-based criteria of evaluating risk models. Fourthly, multivariate framework is developed for estimating (conditional) ES and ES risk contributions (ESC), as a principle of capital allocation. Finally, an empirical study of estimating ES and ESC with backtesting is carried out for historical data from Russell Indices.
Download or read book Capital Allocation for Set Valued Risk Measures written by Francesca Centrone and published by . This book was released on 2019 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce the notion of set-valued Capital Allocation rule, and study Capital allocation principles for multivariate set-valued coherent and convex risk measures. We compare these rules with some of those mostly used for univariate (single-valued) risk measures.
Download or read book Risk Measures and Capital Allocation written by Chun-Ju Wang and published by . This book was released on 2010 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: risk measures, capital allocation, conherency, VaR, expected shortfall, backtesting.
Download or read book Capital Allocation and the Pricing of Financially Intermediated Risks written by Richard D. Phillips and published by . This book was released on 2014 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: Under perfect market conditions, standard capital budgeting theory predicts that the discount rates on projects should reflect only non-diversifiable risk and be constant across firms. However, theoretical research by Froot and Stein (1998), among others, suggests that when firms invest in non-hedgeable assets under conditions where capital is costly, project pricing should reflect the covariability of the project with the firm's existing portfolio, even if this covariability represents non-systematic risk. They argue that their theory is especially applicable to financial institutions pricing intermediated risks. Theoretical research also suggests that the prices of intermediated risks will reflect the capital strain that such risks place on the intermediary and hence reflect implicit allocations of capital to the intermediary's business lines (Myers and Read 2001, Zanjani 2002). We test these theoretical predictions by analyzing the prices of insurance risks for U.S. property-liability insurers over the period 1997-2004. Specifically, we regress insurance price variables on capital allocations by line, measures of insurer insolvency risk, and other risk and control variables. The results provide strong support for theoretical predictions that prices of intermediated risks vary across firms to reflect insolvency risk, marginal capital allocations, and non-systematic covariability.
Download or read book Advances in Finance and Stochastics written by Klaus Sandmann and published by Springer Science & Business Media. This book was released on 2002-04-23 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many areas of finance and stochastics, significant advances have been made since this field of research was opened by Black, Scholes and Merton in 1973. This volume contains a collection of original articles by a number of highly distinguished authors, on research topics that are currently in the focus of interest of both academics and practitioners.
Download or read book The New Palgrave Dictionary of Economics written by and published by Springer. This book was released on 2016-05-18 with total page 7493 pages. Available in PDF, EPUB and Kindle. Book excerpt: The award-winning The New Palgrave Dictionary of Economics, 2nd edition is now available as a dynamic online resource. Consisting of over 1,900 articles written by leading figures in the field including Nobel prize winners, this is the definitive scholarly reference work for a new generation of economists. Regularly updated! This product is a subscription based product.
Download or read book Game Theory Alive written by Anna R. Karlin and published by American Mathematical Soc.. This book was released on 2017-04-27 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities. This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments. The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics. The importance of game-theoretic thinking transcends the academic setting—for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.
