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Author: Kanav Gupta Publisher: ISBN: Category : Languages : en Pages : 53
Book Description
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.
Author: Kanav Gupta Publisher: ISBN: Category : Languages : en Pages : 53
Book Description
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.
Author: Giorgio Ferrari Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
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.
Author: Francesco Menoncin Publisher: ISBN: Category : Languages : en Pages : 43
Book Description
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.
Author: Francesco Menoncin Publisher: Springer Nature ISBN: 3030555283 Category : Business & Economics Languages : en Pages : 239
Book Description
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.
Author: Feng Li Publisher: ISBN: Category : Insurance Languages : en Pages : 120
Book Description
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.
Author: Hyun Jin Jang Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
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.
Author: Horand Gassmann Publisher: World Scientific ISBN: 9814407518 Category : Business & Economics Languages : en Pages : 549
Book Description
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.
Author: Claus Munk Publisher: ISBN: Category : Languages : en Pages : 44
Book Description
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.
Author: Kanav Gupta
Author: Kanav Gupta
Author: Giorgio Ferrari
Author: Francesco Menoncin
Author: Francesco Menoncin
Author: Jinlian Wang
Author: Feng Li
Author: Hyun Jin Jang
Author: Mirela Elena Cara
Author: Horand Gassmann
Author: Claus Munk