Optimal Investment Strategy to Minimize Occupation Time

Economy – Quantitative Finance – Portfolio Management

Scientific paper

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Occupation time, optimal investment, stochastic control, free-boundary problem

Scientific paper

We find the optimal investment strategy to minimize the expected time that an individual's wealth stays below zero, the so-called {\it 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.

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