Minimizing the Probability of Ruin When Consumption is Ratcheted

North American Actuarial Journal
Volume 12, Issue 4, 2008
Erhan Bayraktar PhD & Virginia R. Young PhD, FSA


We assume that an agent’s rate of consumption is ratcheted; that is, it forms a nondecreasing process. We assume that the agent invests in a financial market with one riskless and one risky asset, with the latter’s price following geometric Brownian motion as in the Black-Scholes model. Given the rate of consumption, we act as financial advisers and find the optimal investment strategy for the agent who wishes to minimize his probability of ruin. To solve this minimization problem, we use techniques from stochastic optimal control.

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