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MINIMIZING THE PROBABILITY OF LIFETIME RUIN: TWO RISKLESS ASSETS WITH TRANSACTION COSTS

Part of: Hamilton-Jacobi theories, including dynamic programming Optimality conditions

Published online by Cambridge University Press:  01 July 2019

Xiaoqing Liang  and
Virginia R. Young
Xiaoqing Liang
Affiliation:
Department of Statistics, School of Sciences Hebei University of TechnologyTianjin 300401, People’s Republic of China E-Mail: liangxiaoqing115@hotmail.com
Virginia R. Young*
Affiliation:
Department of Mathematics University of Michigan Ann Arbor, MI, 48109, USA
*
E-Mail: vryoung@umich.edu
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Abstract

We compute the optimal investment strategy for an individual who wishes to minimize her probability of lifetime ruin. The financial market in which she invests consists of two riskless assets. One riskless asset is a money market, and she consumes from that account. The other riskless asset is a bond that earns a higher interest rate than the money market, but buying and selling bonds are subject to proportional transaction costs. We consider the following three cases. (1) The individual is allowed to borrow from both riskless assets; ruin occurs if total imputed wealth reaches zero. Under the optimal strategy, the individual does not sell short the bond. However, she might wish to borrow from the money market to fund her consumption. Thus, in the next two cases, we seek to limit borrowing from that account. (2) We assume that the individual pays a higher rate to borrow than she earns on the money market. (3) The individual is not allowed to borrow from either asset; ruin occurs if both the money market and bond accounts reach zero wealth. We prove that the borrowing rate in case (2) acts as a parameter connecting the two seemingly unrelated cases (1) and (3).

Keywords

Probability of lifetime ruintransaction costsdeterministic controlriskless assetsC58C61G22G11

MSC classification

Primary: 49K10: Free problems in two or more independent variables
Secondary: 49K20: Problems involving partial differential equations 49L20: Dynamic programming method
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 3 , September 2019 , pp. 847 - 883
Copyright
© Astin Bulletin 2019 

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