We reveal an interesting convex duality relationship between two problems: (a) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market; (b) a controller-and-stopper problem, in which the...

We assume that an individual 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. Under a constant rate of consumption, we find the optimal investment strategy for the individual who wishes...

Cao et al. (2021) consider a Stackelberg differential game for insurance under model ambiguity. In the main body of the paper, they measure ambiguity via squared-error divergence; then, in the appendix, they briefly consider entropic divergence. In this paper, we show a strong connection between...