Optimal investment strategy to minimize occupation time
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We find the optimal investment strategy to minimize the expected time that an individual’s wealth stays below zero, the so-called occupation time. The individual consumes at a constant rate and invests in a Black-Scholes financial market consisting of one riskless and one risky asset, with the risky asset’s price process following a geometric Brownian motion. We also consider an extension of this problem by penalizing the occupation time for the degree to which wealth is negative.
KeywordsOccupation time Optimal investment Stochastic control Free-boundary problem
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- Akahori, J. (1995). Some formulae for a new type of path-dependent option. Annals of Applied Probability, 5, 91–99. Google Scholar
- Brémaud, P. (1981). Point Processes and Queues. Berlin: Springer. Google Scholar
- Karatzas, I., & Shreve, S. E. (1991). Brownian Motion and Stochastic Calculus. New York: Springer. Google Scholar
- Karatzas, I., & Shreve, S. E. (1998). Methods of Mathematical Finance. New York: Springer. Google Scholar
- Milevsky, M. A., Moore, K.S., & Young, V. R. (2006). Asset allocation and annuity-purchase strategies to minimize the probability of financial ruin. Mathematical Finance, 16(4), 647–671. Google Scholar
- Moore, K. S., & Young, V. R. (2006). Optimal and simple, nearly optimal rules for minimizing the probability of financial ruin in retirement. North American Actuarial Journal, 10(4), 145–161. Google Scholar
- Neuts, M. F. (1989). Structured Stochastic Matrices of M/G/1 Type and Their Applications. New York: Dekker. Google Scholar