We show how to combine censoring technique for Markov chain and strong stochastic comparison to obtain bounds on rewards and the first passage time. We present the main ideas of the method, the algorithms and their proofs. We obtain a substantial reduction of the state space due to the censoring technique. We also present some numerical results to illustrate the effectiveness of the method.

Hansen and Jagannathan (HJ, 1991) describe restrictions on the volatility of stochastic discount factors (SDFs) that price a given set of asset returns. This paper compares the sampling properties of different versions of HJ bounds that use conditioning information in the form of a given set of lagged instruments. HJ describe one way to use conditioning information. Their approach is to multipl...

We investigate how we can bound a Discrete Time Markov Chain (DTMC) by a stochastic matrix with a low rank decomposition. In the first part of the paper we show the links with previous results for matrices with a decomposition of size 1 or 2. Then we show how the complexity of the analysis for steady-state and transient distributions can be simplified when we take into account the decomposition...

We consider how to use the Bellman residual of the dynamic programming operator to compute suboptimality bounds for solutions to stochastic shortest path problems. Such bounds have been previously established only in the special case that “all policies are proper,” in which case the dynamic programming operator is known to be a contraction, and have been shown to be easily computable only in th...

There is a growing concern in the actuarial literature for the effect of dependence between individual risks Xi on the distribution of the aggregate claim S = X1 + · · · + Xn. Recent work by Dhaene and Goovaerts (Dhaene, J., Goovaerts, M.J., 1996. ASTIN Bulletin 26, 201–212; Dhaene, J., Goovaerts, M.J., 1997. Insurance: Mathematics and Economics 19, 243–253) and Müller (Müller, A., 1997a. Insur...

Online matching has received significant attention over the last 15 years due to its close connection to Internet advertising. As the seminal work of Karp, Vazirani, and Vazirani has an optimal (1 − 1/e) competitive ratio in the standard adversarial online model, much effort has gone into developing useful online models that incorporate some stochasticity in the arrival process. One such popula...

In most practical cases, it is impossible to find an explicit expression for the distribution function of the present value of a sequence of cashflows that are discounted using a stochastic return process. In this article, the authors present an easily computable approximation for this distribution function. The approximation is a distribution function which is, in the sense of convex order, an...

We study the online stochastic matching problem in a form motivated by Internet display advertisement. Recently, Feldman et al. gave an algorithm that achieves 0.6702 competitive ratio, thus breaking through the 1−1/e barrier. One of the questions left open in their work is to obtain a better competitive ratio by generalizing their two suggested matchings (TSM) algorithm to d-suggested matching...

We consider a Jackson-type network, each of whose nodes contains N identical channels with a single server. Upon arriving at a node, a task selects m of the channels at random, and enters the one with the shortest queue. We provide stochastic bounds for the distribution of the state of the network in terms of the behaviour of independent nodes of the same type. The bounds are asymptotically tig...