We consider perpetuities of the form D=B1exp(Y1)+B2exp(Y1+Y2)+⋯, where the Yj’s and Bj’s might be i.i.d. or jointly driven by a suitable Markov chain. We assume that the Yj’s satisfy the so-called Cramér condition with associated root θ∗∈(0,∞) and that the tails of the Bj’s are...

We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous structure as the Black-Scholes model, the widely popular option...

We consider the problem of efficient estimation of tail probabilities of sums of correlated lognormals via simulation. This problem is motivated by the tail analysis of portfolios of assets driven by correlated Black-Scholes models. We propose two estimators that can be rigorously shown to be...

We consider asymptotic expansions for defective and excessive renewal equations that are close to being proper. These expansions are applied to the analysis of processor sharing queues and perturbed risk models, and yield approximations that can be useful in applications where moments are...

We develop importance sampling based efficient simulation techniques for three commonly encountered rare event probabilities associated with random walks having i.i.d. regularly varying increments; namely, 1) the large deviation probabilities, 2) the level crossing probabilities, and 3) the...

We derive a continuous time model for the joint evolution of the mid price and the bid-ask spread from a multiscale analysis of the whole limit order book (LOB) dynamics. We model the LOB as a multiclass queueing system and perform our asymptotic analysis using stylized features observed...

We consider asymptotic expansions for defective and excessive renewal equations that are close to being proper. These expansions are applied to the analysis of processor sharing queues and perturbed risk models, and yield approximations that can be useful in applications where moments are...