This note shows that Machina's (1982) assumption that preferences over lotteries are smooth has some economic implications. We show that Fr echet di erentiability implies that preferences represent second order risk aversion (as well as conditional second order risk aversion). This implies, among other things, that decision makers buy full insurance only at the absence of marginal loading. We a...

2. Summary of the thesis 9 2.1. Di erentiability of convex functions and the respective classes of Banach spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2. Summary of Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3. Decompositions of nonseparable Banach spaces . . . . . . . . . . . . . . . 23 2.4. Summary of ...

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We study the sensitivity, with respect to a time dependent domain Ds, of expectations of functionals of a di usion process stopped at the exit from Ds or normally re ected at the boundary of Ds. We establish a di erentiability result and give an explicit expression for the gradient that allows the gradient to be computed by Monte Carlo methods. Applications to optimal stopping problems and pric...

We study the sensitivity, with respect to a time dependent domain Ds, of expectations of functionals of a di usion process stopped at the exit from Ds or normally re ected at the boundary of Ds. We establish a di erentiability result and give an explicit expression for the gradient that allows the gradient to be computed by Monte Carlo methods. Applications to optimal stopping problems and pric...

In this paper we investigate the strict convexity and the di erentiability properties of the stable norm, which corresponds to the homogenized surface tension for a periodic perimeter homogenization problem (in a regular and uniformly elliptic case). We prove that it is always di erentiable in totally irrational directions, while in other directions, it is di erentiable if and only if the corre...

We consider set valued mappings de ned on a linear normed space with convex closed images in IRn Our aim is to construct selections which are Hadamard directionally di erentiable using some approximation of the mul tifunction The constructions suggested assume existence of a cone approxima tion given by a certain derivative of the mapping The rst one makes use of the properties of Steiner point...

The problem of designing a periodic interface between two materials in such a way that time-harmonic waves di racted from the interface have a speci ed fareld pattern is studied. A minimization problem for the interface is formulated, and it is shown that solutions of constrained bounded variation exist. The di erentiability of the cost functional is then studied, with no restrictions on the sm...

in this paper, using clarke’s generalized directional derivative and di-invexity we introduce new concepts of nonsmooth k-α-di-invex and generalized type i univex functions over cones for a nonsmooth vector optimization problem with cone constraints. we obtain some sufficient optimality conditions and mond-weir type duality results under the foresaid generalized invexity and type i cone-univexi...

Much work paralleling the standard theory of linear di erential equations has been done recently for dynamic equations on time scales, providing a uni ed treatment of the continuous and discrete analysis in this area. One area which is less developed is the theory of series solutions, partly due to the lack of suÆcient di erentiability in a general time scale, and also due to the lack of an ana...