Download or read book Optimal Investment and Consumption Strategy for a Retiree Under Stochastic Force of Mortality written by Kanav Gupta and published by . This book was released on 2020 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: With an increase in the self-driven retirement plans during past few decades, more and more retirees are managing their retirement portfolio on their own. Therefore, they need to know the optimal amount of consumption they can afford each year, and the optimal proportion of wealth they should invest in the financial market. In this project, we study the optimization strategy proposed by Delong and Chen (2016). Their model determines the optimal consumption and investment strategy for a retiree facing (1) a minimum lifetime consumption, (2) a stochastic force of mortality following a geometric Brownian motion process, (3) an annuity income, and (4) non-exponential discounting of future income. We use a modified version of the Cox, Ingersoll, and Ross (1985) model to capture the stochastic mortality intensity of the retiree and, subsequently, determine a new optimal consumption and investment strategy using their framework. We use an expansion method to solve the classic Hamilton-Jacobi-Bellman equation by perturbing the non-exponential discounting parameter using partial differential equations.
Download or read book Optimal Retirement Choice Under Age dependent Force of Mortality written by Giorgio Ferrari and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines the retirement decision, optimal investment, and consumption strategies under an age-dependent force of mortality. We formulate the optimization problem as a combined stochastic control and optimal stopping problem with a random time horizon, featuring three state variables: wealth, labor income, and force of mortality. To address this problem, we transform it into its dual form, which is a finite time horizon, three-dimensional degenerate optimal stopping problem with interconnected dynamics. We establish the existence of an optimal retirement boundary that splits the state space into continuation and stopping regions. Regularity of the optimal stopping value function is derived and the boundary is proved to be Lipschitz continuous, and it is characterized as the unique solution to a nonlinear integral equation, which we compute numerically. In the original coordinates, the agent thus retires whenever her wealth exceeds an age-, labor income- and mortality-dependent transformed version of the optimal stopping boundary. We also provide numerical illustrations of the optimal strategies, including the sensitivities of the optimal retirement boundary concerning the relevant model's parameters.
Download or read book Longevity Assets and Pre Retirement Consumption Portfolio Decisions written by Francesco Menoncin and published by . This book was released on 2015 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive a closed form solution for the optimal consumption/investment problem of an agent whose force of mortality is stochastic and whose financial horizon coincides with a fixed retirement date. The investment set includes a longevity asset, as a derivative on the force of mortality. We explore the optimal choices of a representative agent having Hyperbolic Absolute Risk Aversion preferences on both consumption and final wealth. Our numerical analysis shows that individuals optimally invest a large fraction of their wealth in the longevity asset. In our base scenario, calibrated on real world data, a 60-year old male retiring after 5 years should invest around 88% of his wealth in the longevity asset. Such a percentage decreases as time to retirement decreases. We explore sensitivity of our results to market and individual characteristics.
Download or read book Risk Management for Pension Funds written by Francesco Menoncin and published by Springer Nature. This book was released on 2021-02-09 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a consistent and complete framework for studying the risk management of a pension fund. It gives the reader the opportunity to understand, replicate and widen the analysis. To this aim, the book provides all the tools for computing the optimal asset allocation in a dynamic framework where the financial horizon is stochastic (longevity risk) and the investor's wealth is not self-financed. This tutorial enables the reader to replicate all the results presented. The R codes are provided alongside the presentation of the theoretical framework. The book explains and discusses the problem of hedging longevity risk even in an incomplete market, though strong theoretical results about an incomplete framework are still lacking and the problem is still being discussed in most recent literature.
Download or read book The Impact of Stochastic Interest and Mortality Rates on Ruin Probability and Annuitization Decisions Faced by Retirees written by Jinlian Wang and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ruin Problem in Retirement Under Stochastic Return Rate and Mortality Rate and Its Applications written by Feng Li and published by . This book was released on 2008 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Retirees face a difficult choice between annuitization from insurance firms and self-management or so-called self-annuitization. Self-annuitization could provide a higher consumption by investing more assets on equity market but with a risk that retirees may outlive the income from their self-managed assets. Using the Ornstein-Uhlenbeck stochastic model, also called the Vasicek model, for the rate of return, we focus our study on the ruin probability in retirement. We show how asset mix, initial rate of return, and gender impact the ruin probability in retirement. We derive a recursive formula to calculate an approximate distribution for the present value of the life annuity function under our stochastic model. Finally, we use our model to illustrate how a VaR technique can help determine the optimal consumption for a retiree with a certain tolerance to ruin under different retirement goals.
Download or read book Optimal Investment Heterogeneous Consumption and Best Time for Retirement written by Hyun Jin Jang and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function. The optimal heterogeneous consumption strategies for a class of non-homothetic utility maximizer are shown to consume only basic goods when the wealth is small, to consume basic goods and make savings when the wealth is intermediate, and to consume almost all in luxury goods when the wealth is large. The optimal retirement policy is shown to be both universal, in the sense that all individuals should retire at the same level of marginal utility that is determined only by income, labor cost, discount factor as well as market parameters, and not universal, in the sense that all individuals can achieve the same marginal utility with different utility and wealth. It is also shown that individuals prefer to retire as time goes by if the marginal labor cost increases faster than that of income. The main tools used in analyzing the problem are from PDE and stochastic control theory including variational inequality and dual transformation. We finally conduct the simulation analysis for the featured model parameters to investigate practical and economic implications by providing their figures.
Download or read book Optimal Retirement Investment Strategies Under Health Shocks and Jump Diffusion Processes written by Mirela Elena Cara and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Programming written by Horand Gassmann and published by World Scientific. This book was released on 2013 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows the breadth and depth of stochastic programming applications. All the papers presented here involve optimization over the scenarios that represent possible future outcomes of the uncertainty problems. The applications, which were presented at the 12th International Conference on Stochastic Programming held in Halifax, Nova Scotia in August 2010, span the rich field of uses of these models. The finance papers discuss such diverse problems as longevity risk management of individual investors, personal financial planning, intertemporal surplus management, asset management with benchmarks, dynamic portfolio management, fixed income immunization and racetrack betting. The production and logistics papers discuss natural gas infrastructure design, farming Atlantic salmon, prevention of nuclear smuggling and sawmill planning. The energy papers involve electricity production planning, hydroelectric reservoir operations and power generation planning for liquid natural gas plants. Finally, two telecommunication papers discuss mobile network design and frequency assignment problems.
Download or read book Optimal Consumption and Investment Strategies with Stochastic Interest Rates written by Claus Munk and published by . This book was released on 2004 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We characterize the solution to the consumption and investment problem of a time-additive power utility investor in a continuous-time dynamically complete market with stochastic changes in the opportunity set. It is demonstrated that under stochastic interest rates the investor optimally hedges against changes in the term structure of interest rates by investing in a coupon bond, or portfolio of bonds, with a payment schedule that matches the forward-expected (i.e. certainty equivalent) consumption pattern. This is of conceptual importance since the hedge portfolio only depends on the specic term structure dynamics through the consequences for the optimal consumption pattern. We consider two explicit examples where the term structure dynamics are given by the Vasicek model and a three factor non-Markovian Heath-Jarrow-Morton model.
Download or read book Optimal Consumption and Investment with Labor Income Uncertainty and Endogenous Retirement written by Matthew M. Woolley and published by . This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper characterizes optimal consumption and investment policies for investors with asset return predictability, stochastic labor income and endogenously-determined retirement. We find that the ratio of total wealth-to-labor income (normalized wealth) is the primary determinant of the retirement decision and that at all ages, there exists a critical normalized wealth such that above this wealth, investors retire. We further consider the implications of endogenous retirement on portfolio choice. It is well known that human capital plays a large role in the determination of optimal equity proportion in financial portfolios. By endogenizing retirement, human capital becomes dependent on savings and investment decisions, which in turn depend on human capital. When compared to investors who exogenously retire at age 65, we find that low-wealth investors with the option to time retirement invest more aggressively while investors with slightly greater normalized wealth invest less aggressively prior to retirement. Investors with high normalized wealth behave almost the same as in the exogenous retirement case. This result contrasts the results in two recent papers and is due to the existence of stochastic labor income. Finally, we consider the impact of asset return/labor income correlation and find that equity holdings are nearly completely crowded-out by increased labor income (background) risk.
Download or read book How Should Individuals Make a Retirement Plan in the Presence of Mortality Risks and Consumption Constraints written by Bong-Gyu Jang and published by . This book was released on 2016 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates optimal retirement planning when investors desire to maintain a certain minimum level of consumption, which can be achieved only by a guaranteed income stream after retirement. Our model incorporates the subsistence level in consumption and social securities and defined-contribution retirement pensions, all of which are necessary to guarantee an income stream. Our model shows that the movements of the optimal risky investments might dramatically change with the subsistence level in consumption. Our numerical results show that the risky investment rate in the retirement pension can increase with the risk-free gross return rate and with the risk aversion level when the low risk-free rate and risk aversion level are both low. Furthermore, the risky investment rate in the retirement pension can decrease even when the market condition is favorable.
Download or read book Optimal Investment Consumption and Retirement Decision with Disutility and Borrowing Constraints written by Byung Hwa Lim and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we consider a general consumption, portfolio and retirement optimization problem in which a working investor has borrowing constraints. Closed-form solutions are obtained for the utility maximization problems, and numerical procedures are given for the general utility function under borrowing constraints. Moreover we apply the results to the special utility function, the constant elative risk aversion (CRRA) utility function, and its numerical results suggest that the restriction to borrow future labor income makes the investor retire in a lower critical wealth level than in the case of no borrowing constraints.
Download or read book Planning for Individual Retirement Optimal Consumption Investment and Retirement Timing Under Different Preferences and Habit Persistence written by Felix Hentschel and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Investment Consumption and Retirement Choice Problem with Disutility and Subsistence Consumption Constraints written by Byung Hwa Lim and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.
Download or read book Around the Life Cycle written by Marcus Christian Christiansen and published by . This book was released on 2016 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study a classical continuous-time consumption-investment problem of a power utility investor with deterministic labor income with the important feature that the consumption-investment process is constrained to be deterministic. This is motivated by the design of modern pension schemes of defined contribution type where, typically, the savings rate is constant and the proportional investment in growth stocks is a function of age or time-to-retirement, a so-called life-cycle investment strategy. We derive and study the optimal behavior corresponding to the optimal product design within this realistic family of products with deterministic decision profiles. We also propose a couple of suboptimal deterministic strategies inspired from the optimal stochastic strategy and compare the optimal stochastic control, the optimal deterministic control and the suboptimal deterministic controls in terms of certainty equivalents. The conclusion is that only little is lost by constraining to deterministic strategies and only little is lost by implementing the suboptimal simple explicit strategies rather than the optimal one we derive.
Download or read book Financial Planning and Risk Management for Retirement Optimal Investment consumption Choices Under Multiple Risk Exposures written by Zhisheng Li and published by . This book was released on 2006 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
