scholarly journals Optimal Investment, Consumption and Leisure with an Option to File for Bankruptcy

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 827
Author(s):  
Byung Hwa Lim ◽  
Ho-Seok Lee
Keyword(s):  
Decision Problem ◽  
Optimal Strategies ◽  
Optimal Investment ◽  
Mathematical Finance ◽  
Stopping Times ◽  
Dynamic Programming Method ◽  
Maximization Problem ◽  
Portfolio Decisions ◽  
Discounted Utility ◽  
Utility Maximization Problem

This paper investigates the optimal personal bankruptcy decision of a debtor who participates in the labor market. This paper is based on a mathematical finance model that assumes a Black-Scholes financial market and describes a decision problem as an expected discounted utility maximization problem. Our optimization problem can be cast into a mixed optimal stopping and control problem, and has a symmetry feature with a voluntary retirement decision problem in characterizing the stopping times. To obtain value function and optimal strategies, we use dynamic programming method and transform the relevant nonlinear Bellman equation into a linear equation. Numerical illustrations from our explicit expressions for the optimal strategies reveal how an opportunity to file for bankruptcy affects debtor’s consumption, leisure, and portfolio decisions.

scholarly journals Entry and Exit Decision Problem with Implementation Delay

2008 ◽  
Vol 45 (04) ◽  
pp. 1039-1059 ◽  
Author(s):  
Marius Costeniuc ◽  
Michaela Schnetzer ◽  
Luca Taschini
Keyword(s):  
Decision Problem ◽  
Analytic Solution ◽  
Time Lag ◽  
Probabilistic Approach ◽  
Stopping Time ◽  
Stopping Times ◽  
Maximization Problem ◽  
Entry And Exit ◽  
Brownian Motion With Drift ◽  
Implementation Delay

We study investment and disinvestment decisions in situations where there is a time lagd> 0 from the timetwhen the decision is taken to the timet+dwhen the decision is implemented. In this paper we apply the probabilistic approach to the combined entry and exit decisions under the Parisian implementation delay. In particular, we prove the independence between Parisian stopping times and a general Brownian motion with drift stopped at the stopping time. Relying on this result, we solve the constrained maximization problem, obtaining an analytic solution to the optimal ‘starting’ and ‘stopping’ levels. We compare our results with the instantaneous entry and exit situation, and show that an increase in the uncertainty of the underlying process hastens the decision to invest or disinvest, extending a result of Bar-Ilan and Strange (1996).

scholarly journals Entry and Exit Decision Problem with Implementation Delay

2008 ◽  
Vol 45 (4) ◽  
pp. 1039-1059 ◽  
Author(s):  
Marius Costeniuc ◽  
Michaela Schnetzer ◽  
Luca Taschini
Keyword(s):  
Decision Problem ◽  
Analytic Solution ◽  
Time Lag ◽  
Probabilistic Approach ◽  
Stopping Time ◽  
Stopping Times ◽  
Maximization Problem ◽  
Entry And Exit ◽  
Brownian Motion With Drift ◽  
Implementation Delay

We study investment and disinvestment decisions in situations where there is a time lagd> 0 from the timetwhen the decision is taken to the timet+dwhen the decision is implemented. In this paper we apply the probabilistic approach to the combined entry and exit decisions under the Parisian implementation delay. In particular, we prove the independence between Parisian stopping times and a general Brownian motion with drift stopped at the stopping time. Relying on this result, we solve the constrained maximization problem, obtaining an analytic solution to the optimal ‘starting’ and ‘stopping’ levels. We compare our results with the instantaneous entry and exit situation, and show that an increase in the uncertainty of the underlying process hastens the decision to invest or disinvest, extending a result of Bar-Ilan and Strange (1996).

scholarly journals Bellman equations for terminal utility maximization with general bid and ask prices

2018 ◽  
Vol 38 (1) ◽  
pp. 139-155
Author(s):  
Tomasz Rogala ◽  
Łukasz Stettner
Keyword(s):  
Continuous Time ◽  
Utility Maximization ◽  
Optimal Strategies ◽  
Finite Horizon ◽  
Maximization Problem ◽  
Bellman Equations ◽  
Restricted Number ◽  
Utility Maximization Problem

In the paper we solve a system of Bellman equations for finite horizon continuous time terminal utility maximization problem with general càdlàg bid and ask prices. We assume that we have a restricted number of transactions at time moments we choose. The main result of the paper says that we can find a regular version of solutions to the system of Bellman equations, which enables us to find the form of nearly optimal strategies.

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.

On the properties of dynamic value functions in the problem of optimal investment in incomplete markets

2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Michael Mania ◽  
Revaz Tevzadze
Keyword(s):  
Incomplete Markets ◽  
Real Line ◽  
Value Function ◽  
Optimal Solution ◽  
Optimal Investment ◽  
Maximization Problem ◽  
Value Functions ◽  
Utility Maximization Problem ◽  
The Value Function ◽  
Uniformly Bounded

AbstractWe study the analytical properties of a dynamic value function and of an optimal solution to the utility maximization problem in incomplete markets for utility functions defined on the whole real line. It was shown by Kramkov and Sirbu [Ann. Appl. Probab. 16 (2006), no. 3, 1352–1384] that if the relative risk-aversion coefficient of the utility function defined on the half real line is uniformly bounded away from zero and infinity, then the value function at time

scholarly journals UTILITY THEORY FRONT TO BACK — INFERRING UTILITY FROM AGENTS' CHOICES

2014 ◽  
Vol 17 (03) ◽  
pp. 1450018 ◽  
Author(s):  
ALEXANDER M. G. COX ◽  
DAVID HOBSON ◽  
JAN OBłÓJ
Keyword(s):  
Utility Function ◽  
Utility Theory ◽  
Consistency Condition ◽  
Maximization Problem ◽  
Consumption Pattern ◽  
Investment Strategies ◽  
Inverse Approach ◽  
To Come ◽  
Utility Maximization Problem ◽  
Stochastic Setting

We pursue an inverse approach to utility theory and associated consumption and investment problems. Instead of specifying a utility function and deriving the actions of an agent, we assume that we observe the actions of the agent (i.e. consumption and investment strategies) and ask if it is possible to derive a utility function for which the observed behavior is optimal. We work in continuous time both in a deterministic and stochastic setting. In the deterministic setup, we find that there are infinitely many utility functions generating a given consumption pattern. In the stochastic setting of a geometric Brownian motion market it turns out that the consumption and investment strategies have to satisfy a consistency condition (PDE) if they are to come from a classical utility maximization problem. We show further that important characteristics of the agent such as risk attitudes (e.g., DARA) can be deduced directly from the agent's consumption and investment choices.

scholarly journals A Game Theoretic Look at Life Insurance Underwriting

1980 ◽  
Vol 11 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Jean Lemaire
Keyword(s):  
Cooperative Game ◽  
Life Insurance ◽  
Decision Problem ◽  
Optimal Strategies ◽  
Minimax Criterion ◽  
Game Theoretic ◽  
Optimal Set

The decision problem of acceptance or rejection of life insurance proposals is formulated as a two-person non cooperative game between the insurer and the set of the proposers. Using the minimax criterion or the Bayes criterion, it is shown how the value and the optimal strategies can be computed, and how an optimal set of medical informations can be selected and utilized.

scholarly journals Dual Formulation of the Utility Maximization Problem Under Transaction Costs

2001 ◽  
Vol 11 (4) ◽  
pp. 1353-1383 ◽  
Author(s):  
Griselda Deelstra ◽  
Huyên Pham ◽  
Nizar Touzi
Keyword(s):  
Transaction Costs ◽  
Utility Maximization ◽  
Maximization Problem ◽  
Dual Formulation ◽  
Utility Maximization Problem
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