Robust estimates of certain large deviation probabilities for controlled semi-martingales

Hideo Nagai. "Robust estimates of certain large deviation probabilities for controlled semi-martingales." Banach Center Publications 105.1 (2015): 159-192. <http://eudml.org/doc/282144>.

@article{HideoNagai2015,
abstract = {Motivated by downside risk minimization on the wealth process in an incomplete market model, we have studied in the recent work the asymptotic behavior as time horizon T → ∞ of the minimizing probability that the empirical mean of a controlled semi-martingale falls below a certain level on the time horizon T. This asymptotic behavior relates to a risk-sensitive stochastic control problem in the risk-averse case. Indeed, we obtained an expression of the decay rate of the probability by the Legendre transform of the limit value of the value function of the stochastic control problem, which is characterized as the solution to the H-J-B equation of ergodic type. In the current work we present the results on its robust version, admitting model uncertainty.},
author = {Hideo Nagai},
journal = {Banach Center Publications},
keywords = {large deviation probabilities; controlled semi-martingales; Legendre transform; HJB equation; model uncertainty; risk minimization; wealth process; incomplete market model},
language = {eng},
number = {1},
pages = {159-192},
title = {Robust estimates of certain large deviation probabilities for controlled semi-martingales},
url = {http://eudml.org/doc/282144},
volume = {105},
year = {2015},
}

TY - JOUR
AU - Hideo Nagai
TI - Robust estimates of certain large deviation probabilities for controlled semi-martingales
JO - Banach Center Publications
PY - 2015
VL - 105
IS - 1
SP - 159
EP - 192
AB - Motivated by downside risk minimization on the wealth process in an incomplete market model, we have studied in the recent work the asymptotic behavior as time horizon T → ∞ of the minimizing probability that the empirical mean of a controlled semi-martingale falls below a certain level on the time horizon T. This asymptotic behavior relates to a risk-sensitive stochastic control problem in the risk-averse case. Indeed, we obtained an expression of the decay rate of the probability by the Legendre transform of the limit value of the value function of the stochastic control problem, which is characterized as the solution to the H-J-B equation of ergodic type. In the current work we present the results on its robust version, admitting model uncertainty.
LA - eng
KW - large deviation probabilities; controlled semi-martingales; Legendre transform; HJB equation; model uncertainty; risk minimization; wealth process; incomplete market model
UR - http://eudml.org/doc/282144
ER -