An optimal consumption problem in finite time with a constraint on the ruin probability

In this paper, we investigate the following problem: For a given upper bound for the ruin probability, maximize the expected discounted consumption of an investor in finite time. The endowment of the agent is modeled by a Brownian motion with positive drift. We give an iterative algorithm for the so...

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Bibliographic Details
Published in:Finance and stochastics Vol. 19; no. 4; pp. 791 - 847
Main Author: Grandits, Peter
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2015
Springer Nature B.V
Subjects:
Algorithms
Boundary value problems
Brownian motion
Consumption
Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Endowment
Finance
Grammatical aspect
Insurance
Investments
Management
Mathematical analysis
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Quantitative Finance
Statistics for Business
Studies
Utility functions
Viscosity
49J20
Singular control problem
Optimal consumption
45J05
35R37
Free boundary value problem
C61
ISSN:0949-2984, 1432-1122
Online Access:Get full text
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Summary:In this paper, we investigate the following problem: For a given upper bound for the ruin probability, maximize the expected discounted consumption of an investor in finite time. The endowment of the agent is modeled by a Brownian motion with positive drift. We give an iterative algorithm for the solution of the problem, where in each step an unconstrained, but penalized problem is solved. For the discontinuous value function V ( t , x ) of the penalized problem, we show that it is the unique viscosity solution of the corresponding Hamilton–Jacobi–Bellman equation. Moreover, we characterize the optimal strategy as a barrier strategy with continuous barrier function.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-015-0275-x