3,357 research outputs found
Conditioning an additive functional of a markov chain to stay non-negative. I, Survival for a long time
Let (X-t)(t >= 0) be a continuous-time irreducible Markov chain on a finite state space E, let v be a map v: E -> R \ {0}, and let (phi(t))(t >= 0) be an additive functional defined by phi(t) = integral(0)(t)(X-s) ds. We consider the case in which the process (phi(t))(t >= 0) is oscillating and that in which (phi(t))(t >= 0) has a negative drift. In each of these cases, we condition the process (X-t, phi(t))(t >= 0) on the event that (phi(t))(t >= 0) is nonnegative until time T and prove weak convergence of the conditioned process as T -> infinity
Game-theoretic approach to risk-sensitive benchmarked asset management
In this article we consider a game theoretic approach to the Risk-Sensitive
Benchmarked Asset Management problem (RSBAM) of Davis and Lleo \cite{DL}. In
particular, we consider a stochastic differential game between two players,
namely, the investor who has a power utility while the second player represents
the market which tries to minimize the expected payoff of the investor. The
market does this by modulating a stochastic benchmark that the investor needs
to outperform. We obtain an explicit expression for the optimal pair of
strategies as for both the players.Comment: Forthcoming in Risk and Decision Analysis. arXiv admin note: text
overlap with arXiv:0905.4740 by other author
On the regularity of American options with regime-switching uncertainty
We study the regularity of the stochastic representation of the solution of a
class of initial-boundary value problems related to a regime-switching
diffusion. This representation is related to the value function of a
finite-horizon optimal stopping problem such as the price of an American-style
option in finance. We show continuity and smoothness of the value function
using coupling and time-change techniques. As an application, we find the
minimal payoff scenario for the holder of an American-style option in the
presence of regime-switching uncertainty under the assumption that the
transition rates are known to lie within level-dependent compact sets.Comment: 22 pages, to appear in Stochastic Processes and their Application
Monotonicity of the value function for a two-dimensional optimal stopping problem
We consider a pair of stochastic processes satisfying the equation
driven by a Brownian motion and study the monotonicity and
continuity in of the value function
, where the supremum is taken
over stopping times with respect to the filtration generated by . Our
results can successfully be applied to pricing American options where is
the discounted price of an asset while is given by a stochastic volatility
model such as those proposed by Heston or Hull and White. The main method of
proof is based on time-change and coupling.Comment: Published in at http://dx.doi.org/10.1214/13-AAP956 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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