Maintaining cost and ruin probability

Specialized funds such as charitable trusts do not attach much value to consumption, instead, they pursue to maintain a satisfactory level of spending and avoid ruin to achieve their managerial goals. We employ an objective function tailored for studying ruin probability of a specialized fund, which implies simple analytical conditions to judge if the fund can be operable permanently. We analytically show that even if the fund has fixed portfolio weights and faces both fixed and proportional maintaining cost, there may still exist a positive probability for the fund to maintain operability permanently. Since if the stock is profitable enough, the wealth process has a large positive drift to offset effects of the fixed cost and downside risk. We extend the benchmark model to a case allowing portfolio rebalance between risky assets, and also obtain analytical expressions for optimal portfolio choices and ruin probability. Allowing portfolio selection potentially improves survival probability. Finally, we provide conditions needed to enjoy a positive probability of permanent survival when the fund can invest in a short bond (potentially with a risky asset) with stochastic nominal riskless interest rate.