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Optimal Portfolio Selection with Life Insurance Under Inflation Risk

Optimal Portfolio Selection with Life Insurance Under Inflation Risk
Author: Minsuk Kwak
Publisher:
Total Pages:
Release: 2014
Genre:
ISBN:

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This paper investigates a continuous-time optimal consumption, investment, and life insurance decision problem of a family under inflation risk. In the financial market, there is a liquid inflation-linked index bond market which can be utilized to hedge the inflation risk. The explicit solutions for the optimal strategies including consumption rate, investment for each financial asset, and life insurance premium are derived for constant relative risk aversion (CRRA) utility case using martingale approach. The roles of an index bond are investigated and it is verified that they depend on market parameters. We analyze the effects of market parameters on the optimal strategies with focus on the demand for index bond and optimal life insurance premium. Especially, the change of inflation rate has considerable impact on optimal life insurance premium.


Strategic Asset Allocation

Strategic Asset Allocation
Author: John Y. Campbell
Publisher: OUP Oxford
Total Pages: 272
Release: 2002-01-03
Genre: Business & Economics
ISBN: 019160691X

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Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.


Stochastic Optimal Portfolios and Life Insurance Problems in a Le̹vy Market

Stochastic Optimal Portfolios and Life Insurance Problems in a Le̹vy Market
Author: Calisto Guambe
Publisher:
Total Pages:
Release: 2018
Genre:
ISBN:

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This thesis solves various optimal investment, consumption and life insurance problems described by jump-diffusion processes. In the first part of the thesis, we solve an optimal investment, consumption, and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic volatility. Using the martingale approach, we prove the existence of the optimal strategy and the optimal martingale measure and we obtain the explicit solutions for the power utility functions. Secondly, we prove the sufficient and necessary maximum principle for the similar problem proposed in the first part. Then we apply the results to solve an investment, consumption, and life insurance problem with stochastic volatility, that is, we consider a wage earner investing in one risk-free asset and one risky asset described by a jump-diffusion process and has to decide concerning consumption and life insurance purchase. We assume that the life insurance for the wage earner is bought from a market composed of M > 0 life insurance companies offering pairwise distinct life insurance contracts. The goal is to maximize the expected utilities derived from the consumption, the legacy in the case of a premature death and the investor's terminal wealth. The third part discusses an optimal investment, consumption and insurance problem of a wage earner under inflation. Assume a wage earner investing in a real money account and three asset prices, namely: a real zero coupon bond, the inflation-linked real money account and a risky share described by jump-diffusion processes. Using the theory of quadratic-exponential backward stochastic differential equation (BSDE) with jumps approach, we derive the optimal strategy for the two typical utilities (exponential and power) and the value function is characterized as a solution of BSDE with jumps. The explicit solutions for the optimal investment in both cases of exponential and power utility functions for a diffusion case are derived.


Applied Stochastic Control of Jump Diffusions

Applied Stochastic Control of Jump Diffusions
Author: Bernt Øksendal
Publisher: Springer Science & Business Media
Total Pages: 263
Release: 2007-04-26
Genre: Mathematics
ISBN: 3540698264

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Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.


Portfolio Choice and Life Insurance

Portfolio Choice and Life Insurance
Author: Moshe A. Milevsky
Publisher:
Total Pages: 31
Release: 2009
Genre:
ISBN:

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We study a class of portfolio choice problems that combine life insurance and labor income under constant relative risk aversion preferences (CRRA) preferences for consumption, within the optimal control framework pioneered by Merton (1969, 1971). Our model differs from previous research by (i) focusing attention on the correlation between human capital and financial capital, and (ii) modeling the utility of the family as opposed to separating consumption and bequest. From a technical point of view we show how the underlying Hamilton-Jacobi-Bellman (HJB) equation can be simplified using a similarity reduction technique, which then allows for the implementation of an efficient numerical solution. And, for reasonable financial economic parameter values, a closed-form approximation is derived which greatly simplifies the numerical calculations. A variety of example illustrating our numerical algorithm are also provided. Our main qualitative result is that households whose primary breadwinner's wages are negatively correlated with financial market returns, should optimally purchase more life insurance and can afford to take more risky positions with their financial portfolio. In addition, we find that the optimal face value of life insurance is remarkably insensitive to the family's risk aversion.


Risk Management for Pension Funds

Risk Management for Pension Funds
Author: Francesco Menoncin
Publisher: Springer Nature
Total Pages: 239
Release: 2021-02-09
Genre: Business & Economics
ISBN: 3030555283

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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.


Optimal Portfolio Choice in Retirement with Participating Life Annuities

Optimal Portfolio Choice in Retirement with Participating Life Annuities
Author: Ralph Rogalla
Publisher:
Total Pages: 31
Release: 2014
Genre:
ISBN:

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This paper derives optimal consumption, investment, and annuitization patterns for retired households that have access to German-style participating payout life annuities (PLAs), allowing for capital market risks as well as idiosyncratic and systematic longevity risks. PLAs provide guaranteed minimum benefits in combination with participation in insurers' surpluses. Minimum benefits are calculated based on conservative assumptions regarding capital market and mortality developments, while surpluses distributed to annuitants bridge the gap between the insurers' actual investment and mortality experiences and the projections used in pricing. Through the participation scheme, systematic longevity risk is shared between insurers and annuitants, as unanticipated longevity shocks result in benefit adjustments via the surplus mechanism.We show that the retiree draws substantial utility from access to PLAs, equivalent to 20 percent of initial wealth in the presence of systematic longevity risk. We also find that stochasticity in mortality rates only has minor impact on the appeal of PLAs to the retiree. Even if the interest rate guarantee is reduced to zero in adverse capital market environments, PLAs prove to provide substantial utility for retirees. Overall, the participating life annuity design produces substantial welfare gains over a no-annuity world, while being an efficient setup that helps providers to hedge long-term risks that are difficult to hedge otherwise, such as systematic longevity risks.


Risk Analysis and Portfolio Modelling

Risk Analysis and Portfolio Modelling
Author: Elisa Luciano
Publisher: MDPI
Total Pages: 224
Release: 2019-10-16
Genre: Business & Economics
ISBN: 3039216244

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Financial Risk Measurement is a challenging task, because both the types of risk and the techniques evolve very quickly. This book collects a number of novel contributions to the measurement of financial risk, which address either non-fully explored risks or risk takers, and does so in a wide variety of empirical contexts.