PORTFOLIO OPTIMIZATION WITH PERFORMANCE RATIOS

Hongcan Lin (), David Saunders () and Chengguo Weng
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Hongcan Lin: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo N2L 3G1, Canada
David Saunders: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo N2L 3G1, Canada
Chengguo Weng: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo N2L 3G1, Canada

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 05, 1-38

Abstract: We consider the portfolio selection problem of maximizing a performance measure in a continuous-time diffusion model. The performance measure is the ratio of the overperformance to the underperformance of a portfolio relative to a benchmark. Following a strategy from fractional programming, we analyze the problem by solving a family of related problems, where the objective functions are the numerator of the original problem minus the denominator multiplied by a penalty parameter. These auxiliary problems can be solved using the martingale method for stochastic control. The existence of solution is discussed in a general setting and explicit solutions are derived when both the reward and the penalty functions are power functions.

Keywords: Performance ratio; portfolio optimization; stochastic control; martingale method (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024919500225

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