caa a22 4500 445363290 CHVBK 20180317142921.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00780-011-0160-1 doi (NATIONALLICENCE)springer-10.1007/s00780-011-0160-1 Proving regularity of the minimal probability of ruin via a game of stopping and control [Elektronische Daten] [Erhan Bayraktar, Virginia Young] 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 the individual can invest in a Black-Scholes financial market; (b)acontroller-and-stopper problem, in which the controller controls the drift and volatility of a process in order to maximize a running reward based on that process, and the stopper chooses the time to stop the running reward and pays the controller a final amount at that time. Our primary goal is to show that the minimal probability of ruin, whose stochastic representation does not have a classical form as does the utility maximization problem (i.e., the objective's dependence on the initial values of the state variables is implicit), is the unique classical solution of its Hamilton-Jacobi-Bellman (HJB) equation, which is a non-linear boundary-value problem. We establish our goal by exploiting the convex duality relationship between (a) and (b). Springer-Verlag, 2011 Probability of lifetime ruin nationallicence Stochastic games nationallicence Optimal stopping nationallicence Optimal investment nationallicence Viscosity solution nationallicence Hamilton-Jacobi-Bellman equation nationallicence Variational inequality nationallicence Bayraktar Erhan Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA aut Young Virginia Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA aut Finance and Stochastics Springer-Verlag 15/4(2011-12-01), 785-818 0949-2984 15:4<785 2011 15 780 https://doi.org/10.1007/s00780-011-0160-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00780-011-0160-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bayraktar Erhan Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA aut NATIONALLICENCE 700 1- Young Virginia Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA aut NATIONALLICENCE 773 0- Finance and Stochastics Springer-Verlag 15/4(2011-12-01), 785-818 0949-2984 15:4<785 2011 15 780 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer