Skip to main content Accessibility help
×
Home

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

  • Xiaoqing Liang (a1) and Virginia R. Young (a2)

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).

Copyright

Corresponding author

References

Hide All
Azcue, P. and Muler, N (2013) Minimizing the ruin probability allowing investments in two assets: A two-dimensional problem. Mathematical Methods of Operations Research, 77(2), 177206.
Azcue, P and Muler, N (2014) Stochastic Optimization in Insurance: A Dynamic Programming Approach. New York: Springer.
Bayraktar, E., David Promislow, S. and Young, V.R. (2016) Purchasing life insurance to reach a bequest goal while consuming. SIAM Journal on Financial Mathematics, 7(1), 183214.
Bayraktar, E. and Young, V.R. (2007) Minimizing the probability of lifetime ruin under borrowing constraints. Insurance: Mathematics and Economics, 41(1), 196221.
Bayraktar, E. and Young, V.R. (2016) Optimally investing to reach a bequest goal. Insurance: Mathematics and Economics, 70, 110.
Bayraktar, E. and Zhang, Y (2015a) Minimizing the probability of lifetime ruin under ambiguity aversion. SIAM Journal on Control and Optimization, 53(1), 5890.
Bayraktar, E. and Zhang, Y (2015b) Stochastic Perron’s method for the probability of lifetime ruin problem under transaction costs. SIAM Journal on Control and Optimization, 53(1), 91113.
Browne, S. (1997) Survival and growth with a liability: Optimal portfolio strategies in continuous time. Mathematics of Operations Research, 22(2), 468493.
Constantinides, G. (1986). Capital market equilibrium with transaction costs. Journal of Political Economy, 94(4), 842862.
Davis, M.H.A. and Norman, A.R. (1990). Portfolio selection with transaction costs. Mathematics of Operations Research, 15(4), 676713.
Delgado, F., Dumas, B. and Puopolo, GW. (2015) Hysteresis bands on returns, holding period and transaction costs. Journal of Banking and Finance, 57, 86100.
Hipp, C. and Plum, M. (2000) Optimal investment for insurers. Insurance: Mathematics and Economics, 27(2), 215228.
Kallsen, J. and Muhle-Karbe, J. (2017) The general structure of optimal investment and consumption with small transaction costs. Mathematical Finance, 27(3), 659703.
Liang, X. and Young, V.R. (2018) Minimizing the probability of ruin: Two riskless assets with transaction costs and proportional reinsurance. Statistics and Probability Letters, 140, 167175.
Magill, M.J.P. and Constantinides, G. (1976) Portfolio selection with transaction costs. Journal of Economic Theory, 13(2), 245263.
Milevsky, M.A., Moore, K.S. and Young, V.R. (2006) Asset allocation and annuity-purchase strategies to minimize the probability of financial ruin. Mathematical Finance, 16(4), 647671.
Pestien, V.C. and Sudderth, W.D. (1985) Continuous-time red and black: How to control a diffusion to a goal. Mathematics of Operations Research, 10(4), 599611.
Shreve, S.E., Mete Soner, H. and Xu, G.-L. (1991). Optimal investment and consumption with two bonds and transaction costs. Mathematical Finance, 1(3), 5384.
Thonhauser, S. (2013) Optimal investment under transaction costs for an insurer. European Actuarial Journal, 3(2), 359383.
Vayanos, D. and Vila, J.-L. (1999) Equilibrium interest rate and liquidity premium with transaction costs. Economic Theory, 13(3), 509539.
Wang, T. and Young, V.R. (2012) Optimal commutable annuities to minimize the probability of lifetime ruin. Insurance: Mathematics and Economics, 50(1), 200216.
Yang, Z. and Huang, L. (2004) Optimal portfolio strategies with a liability and random risk: the case of different lending and borrowing rates. Journal of Applied Mathematics and Computing, 15(1–2), 109126.
Young, V.R. (2004) Optimal investment strategy to minimize the probability of lifetime ruin. North American Actuarial Journal, 8(4), 105126.
Zariphopoulou, T. (1991) An optimal investment/consumption model with borrowing. Mathematics of Operations Research, 16(4), 802822.
Zariphopoulou, T. (1992) Investment-consumption models with transaction fees and Markovchain parameters. SIAM Journal on Control and Optimization, 30(3), 613636.

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed