<Para ID="Par1">Equivalent characterizations of multi-portfolio time consistency are deduced for closed convex and coherent set-valued risk measures on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$L^{p}({\varOmega,\mathcal{F},\mathbb{P}; \mathbb{R}^{d}})$</EquationSource> </InlineEquation> with image space in the power set of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$L^{p}({\varOmega,\mathcal{F}_{t},\mathbb{P};...</equationsource></inlineequation></equationsource></inlineequation></para>

<Para ID="Par1">We price a contingent claim liability (claim for short) using a utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a...</para>

<Para ID="Par1">We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function g of the terminal wealth. The manager’s own utility function U is assumed to be smooth and strictly concave;...</para>