TY - JOUR
T1 - Stochastic dominance for sequences and implied utility in dynamic optimization
AU - Dentcheva, Darinka
AU - Ruszczyński, Andrzej
PY - 2008
Y1 - 2008
N2 - We introduce a stochastic dynamic optimization problem, where risk aversion is expressed by a stochastic ordering constraint. The constraint requires that a random reward sequence depending on our decisions dominates a given benchmark random sequence. The dominance is defined by discounting both processes with a family of discount sequences, and by applying a univariate order. We describe the generator of this order. We develop necessary and sufficient conditions of optimality for convex stochastic control problems with the new ordering constraint and we derive an equivalent control problem featuring implied utility functions.
AB - We introduce a stochastic dynamic optimization problem, where risk aversion is expressed by a stochastic ordering constraint. The constraint requires that a random reward sequence depending on our decisions dominates a given benchmark random sequence. The dominance is defined by discounting both processes with a family of discount sequences, and by applying a univariate order. We describe the generator of this order. We develop necessary and sufficient conditions of optimality for convex stochastic control problems with the new ordering constraint and we derive an equivalent control problem featuring implied utility functions.
KW - Risk
KW - Stochastic control
KW - Stochastic orders
KW - Stochastic programming
KW - Utility
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UR - http://www.scopus.com/inward/citedby.url?scp=57549117458&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:57549117458
SN - 1310-1331
VL - 61
SP - 15
EP - 22
JO - Comptes Rendus de L'Academie Bulgare des Sciences
JF - Comptes Rendus de L'Academie Bulgare des Sciences
IS - 1
ER -