We consider the question of an optimal transaction between two investors to minimize their risks. We define a dynamic entropic risk measure using backward stochastic differential equations related to a continuous-time single jump process. The inf-convolution of dynamic entropic risk measures is a key transformation in solving the optimization problem.
"Optimal design of dynamic default risk measures." J. Appl. Probab. 49 (4) 967 - 977, December 2012. https://doi.org/10.1239/jap/1354716651