Author: Anne Balter Publisher: ISBN: Category : Languages : en Pages : 35
Book Description
We study portfolio choice in a Black-Scholes world under drift uncertainty. Preferences towards risk and ambiguity are modeled using the smooth ambiguity approach under a double power utility assumption and a normal distribution assumption on the unknown drift. Optimal investment in this setting is time-inconsistent: While utility is maximized by a precommitment strategy resembling the classical Merton solution, the investor's future selves prefer to constantly increase the riskiness of the strategy. In contrast, the optimal dynamically consistent investment strategy accounts for variations in the perceived severity of drift uncertainty, thus increasing the riskiness of the strategy gradually over time. We provide a detailed comparative analysis of the mechanics and interplay of ambiguity, myopia and optimal decisions in this setting. We show that an investor who pre-commits will regret that decision from some time point onwards, wishing that she had followed the dynamically consistent strategy. This “point of regret” always lies near the middle of the investment horizon.
Author: Sigrid Källblad Publisher: ISBN: Category : Languages : en Pages : 41
Book Description
We combine forward investment performance processes and ambiguity averse portfolio selection. We introduce the notion of robust forward criteria which addresses the issues of ambiguity in model specification and in preferences and investment horizon specification. It describes the evolution of time-consistent ambiguity averse preferences. We first focus on establishing dual characterizations of the robust forward criteria. This offers various advantages as the dual problem amounts to a search for an infimum whereas the primal problem features a saddle-point. Our approach is based on ideas developed in Schied (2007) and Zitkovic (2009). We then study in detail non-volatile criteria. In particular, we solve explicitly the example of an investor who starts with a logarithmic utility and applies a quadratic penalty function. The investor builds a dynamical estimate of the market price of risk and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated with the investor's estimate. The leverage is proportional to the investor's confidence in her estimate.
Author: Hui Zhao Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This paper studies the optimal investment and benefit adjustment problem for a collective DC (CDC) pension plan in an environment with parameter uncertainty. We propose a smooth ambiguity framework to model the pension trustee's preferences towards risk and ambiguity. Since the pension trustee is ambiguous about the risky assets, she/he decides to invest in a risk-free asset, a purely risky asset and an ambiguous risky asset whose return is uncertain. Furthermore, we take the stochastic salary into account. The objective is to maximize the expectation of the accumulated benefit payment and terminal wealth under a smooth ambiguity utility which is the double power form. The utility function makes the problem time-inconsistent and we establish the extended HJB equation via game theoretic formulation. The equilibrium strategy and equilibrium value function are derived under smooth ambiguity. Finally, sensitivity analysis is provided to demonstrate the effects of model parameters on the equilibrium investment and benefit adjustment strategies.
Author: L. C. G. Rogers Publisher: Springer Science & Business Media ISBN: 3642352022 Category : Mathematics Languages : en Pages : 163
Book Description
Readers of this book will learn how to solve a wide range of optimal investment problems arising in finance and economics. Starting from the fundamental Merton problem, many variants are presented and solved, often using numerical techniques that the book also covers. The final chapter assesses the relevance of many of the models in common use when applied to data.
Author: David Schröder Publisher: ISBN: Category : Languages : en Pages : 40
Book Description
Recent literature on optimal investment has stressed the difference between the impact of risk and the impact of ambiguity - also called Knightian uncertainty - on investors' decisions. In this paper, we show that a decision maker's attitude towards ambiguity is similarly crucial for investment decisions. We capture the investor's individual ambiguity attitude by applying alpha-MEU preferences to a standard investment problem. We show that the presence of ambiguity often leads to an increase in the subjective project value, and entrepreneurs are more eager to invest. Thereby, our investment model helps to explain differences in investment behavior in situations which are objectively identical.
Author: Julian Hölzermann Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This paper studies dynamic asset allocation with interest rate risk and several sources of ambiguity. The market consists of a risk-free asset, a zero-coupon bond (both determined by a Vasicek model), and a stock. There is ambiguity about the risk premia, the volatilities, and the correlation. The investor's preferences display both risk aversion and ambiguity aversion. The optimal investment problem can be solved in closed-form under typical market conditions. The solution shows that the investor does not hedge ambiguity but only risk, while the ambiguity only affects the speculative motives of the investor. An implementation of the optimal investment strategy shows the impact of the different sources of ambiguity. Ambiguity aversion helps to tame the highly leveraged portfolios neglecting ambiguity and leads to strategies that are more in line with popular investment advice. The solution method for the optimal investment problem is based on an extension of the martingale optimality principle.
Author: Leonard C. MacLean Publisher: World Scientific ISBN: 9814417351 Category : Business & Economics Languages : en Pages : 941
Book Description
This handbook in two parts covers key topics of the theory of financial decision making. Some of the papers discuss real applications or case studies as well. There are a number of new papers that have never been published before especially in Part II.Part I is concerned with Decision Making Under Uncertainty. This includes subsections on Arbitrage, Utility Theory, Risk Aversion and Static Portfolio Theory, and Stochastic Dominance. Part II is concerned with Dynamic Modeling that is the transition for static decision making to multiperiod decision making. The analysis starts with Risk Measures and then discusses Dynamic Portfolio Theory, Tactical Asset Allocation and Asset-Liability Management Using Utility and Goal Based Consumption-Investment Decision Models.A comprehensive set of problems both computational and review and mind expanding with many unsolved problems are in an accompanying problems book. The handbook plus the book of problems form a very strong set of materials for PhD and Masters courses both as the main or as supplementary text in finance theory, financial decision making and portfolio theory. For researchers, it is a valuable resource being an up to date treatment of topics in the classic books on these topics by Johnathan Ingersoll in 1988, and William Ziemba and Raymond Vickson in 1975 (updated 2 nd edition published in 2006).
Author: A. Bensoussan Publisher: IOS Press ISBN: 161499238X Category : Business & Economics Languages : en Pages : 296
Book Description
Financial engineering has become the focus of widespread media attention as a result of the worldwide financial crisis of recent years. This book is the second in a series dealing with financial engineering from Ajou University in Korea. The main objective of the series is to disseminate recent developments and important issues in financial engineering to graduate students and researchers, and to provide surveys or pedagogical exposition of important published papers in a broad perspective, as well as analyses of important financial news concerning financial engineering research, practices or regulations. Real Options, Ambiguity, Risk and Insurance, comprises 12 chapters and is divided into three parts. In Part I, five chapters deal with real options analysis, which addresses the issue of investment decisions in complex, innovative or risky projects. Part II presents three chapters on ambiguity. The notion of ambiguity is one of the major breakthroughs in the expected utility theory; ambiguity arises as uncertainties cannot be precisely described in the probability space. Part III consists of four chapters devoted to risk and insurance, and covers mutual insurance for non-traded risks, downside risk management, and credit risk in fixed income markets. This volume will be useful to both graduate students and researchers in understanding relatively new areas in economics and finance, as well as challenging aspects of mathematics.
Author: Anne Balter
Author: Sigrid Källblad
Author: Hui Zhao
Author: L. C. G. Rogers
Author: David Schröder
Author: Thomas Knispel
Author: Julian Hölzermann
Author: 
Author: Leonard C. MacLean
Author: A. Bensoussan