scholarly journals Optimal investment with intermediate consumption under no unbounded profit with bounded risk

2017 ◽  
Vol 54 (3) ◽  
pp. 710-719 ◽  
Author(s):  
Huy N. Chau ◽  
Andrea Cosso ◽  
Claudio Fontana ◽  
Oleksii Mostovyi
Keyword(s):  
Utility Maximization ◽  
Optimal Investment ◽  
Incomplete Market ◽  
Value Functions ◽  
Stochastic Field ◽  
Intermediate Consumption ◽  
Bounded Risk ◽  
Primal And Dual

Abstract We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the utility maximization theory hold under the assumptions of no unbounded profit with bounded risk and of the finiteness of both primal and dual value functions.

scholarly journals Kim and Omberg Revisited: The Duality Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Anna Battauz ◽  
Marzia De Donno ◽  
Alessandro Sbuelz
Keyword(s):  
Expected Utility ◽  
Explicit Solution ◽  
Utility Maximization ◽  
Optimal Investment ◽  
Incomplete Market ◽  
Maximization Problem ◽  
Expected Utility Maximization ◽  
Duality Approach ◽  
Utility Maximization Problem ◽  
Optimal Investment Problem

We give an alternative duality-based proof to the solution of the expected utility maximization problem analyzed by Kim and Omberg. In so doing, we also provide an example of incomplete-market optimal investment problem for which the duality approach is conducive to an explicit solution.

Nonconcave Utility Maximization with Portfolio Bounds

2021 ◽  
Author(s):  
Min Dai ◽  
Steven Kou ◽  
Shuaijie Qian ◽  
Xiangwei Wan
Keyword(s):  
Finite Difference ◽  
Behavioral Economics ◽  
Difference Scheme ◽  
Viscosity Solution ◽  
Finite Difference Scheme ◽  
Utility Maximization ◽  
Utility Functions ◽  
Value Functions ◽  
Incentive Schemes ◽  
Definition Of

The problems of nonconcave utility maximization appear in many areas of finance and economics, such as in behavioral economics, incentive schemes, aspiration utility, and goal-reaching problems. Existing literature solves these problems using the concavification principle. We provide a framework for solving nonconcave utility maximization problems, where the concavification principle may not hold, and the utility functions can be discontinuous. We find that adding portfolio bounds can offer distinct economic insights and implications consistent with existing empirical findings. Theoretically, by introducing a new definition of viscosity solution, we show that a monotone, stable, and consistent finite difference scheme converges to the value functions of the nonconcave utility maximization problems. This paper was accepted by Agostino Capponi, finance.

scholarly journals Legendre Transform-Dual Solution for a Class of Investment and Consumption Problems with HARA Utility

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hao Chang ◽  
Xi-min Rong
Keyword(s):  
Absolute Risk ◽  
Optimal Investment ◽  
Dynamic Programming Principle ◽  
Legendre Transform ◽  
Power Utility ◽  
Transform Method ◽  
Intermediate Consumption ◽  
Special Cases ◽  
Hara Utility ◽  
Optimal Investment And Consumption

This paper provides a Legendre transform method to deal with a class of investment and consumption problems, whose objective function is to maximize the expected discount utility of intermediate consumption and terminal wealth in the finite horizon. Assume that risk preference of the investor is described by hyperbolic absolute risk aversion (HARA) utility function, which includes power utility, exponential utility, and logarithm utility as special cases. The optimal investment and consumption strategy for HARA utility is explicitly obtained by applying dynamic programming principle and Legendre transform technique. Some special cases are also discussed.

Martingale and Duality Methods for Utility Maximization in an Incomplete Market

1991 ◽  
Vol 29 (3) ◽  
pp. 702-730 ◽  
Author(s):  
Ioannis Karatzas ◽  
John P. Lehoczky ◽  
Steven E. Shreve ◽  
Gan-Lin Xu
Keyword(s):  
Utility Maximization ◽  
Incomplete Market ◽  
Duality Methods

scholarly journals MAX–MIN OPTIMIZATION PROBLEM FOR VARIABLE ANNUITIES PRICING

2015 ◽  
Vol 18 (08) ◽  
pp. 1550053 ◽  
Author(s):  
CHRISTOPHETTE BLANCHET-SCALLIET ◽  
ETIENNE CHEVALIER ◽  
IDRIS KHARROUBI ◽  
THOMAS LIM
Keyword(s):  
Expected Utility ◽  
Utility Maximization ◽  
Optimization Problem ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Worst Case ◽  
Variable Annuities ◽  
Minimization Problems ◽  
Optimal Investment Strategy ◽  
Utility Indifference

In this paper, we study the valuation of variable annuities for an insurer. We concentrate on two types of these contracts, namely guaranteed minimum death benefits and guaranteed minimum living benefits that allow the insured to withdraw money from the associated account. Here, the price of variable annuities corresponds to a fee, fixed at the beginning of the contract, that is continuously taken from the associated account. We use a utility indifference approach to determine the indifference fee rate. We focus on the worst case for the insurer, assuming that the insured makes the withdrawals that minimize the expected utility of the insurer. To compute this indifference fee rate, we link the utility maximization in the worst case for the insurer to a sequence of maximization and minimization problems that can be computed recursively. This allows to provide an optimal investment strategy for the insurer when the insured follows the worst withdrawal strategy and to compute the indifference fee. We finally explain how to approximate these quantities via the previous results and give numerical illustrations of parameter sensitivity.

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