Dual risk models are popular for modeling a venture capital or high tech company, for which the running cost is deterministic and the profits arrive stochastically over time. Most of the existing literature on dual risk models concentrated on the optimal dividend strategies. In this paper, we...

The editors of this special issue and several of the contributing authors have known Peter for a long time. We thought that the special issue will be enriched by adding a few personal notes and recollections about our interactions with Peter.

Dual risk models are popular for modeling a venture capital or high-tech company, for which the running cost is deterministic and the profits arrive stochastically over time. Most of the existing literature on dual risk models concentrates on the optimal dividend strategies. In this paper, we...

In this short paper, we study the asymptotics for the price of call options for very large strikes and put options for very small strikes. The stock price is assumed to follow the Black-Scholes models. We analyze European, Asian, American, Parisian and perpetual options and conclude that the...

One popular approach to model the limit order books dynamics of the best bid and ask at level-1 is to use the reduced-form diffusion approximations. It is well known that the biggest contributing factor to the price movement is the imbalance of the best bid and ask. We investigate the data of...

We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations, however convergence may be exponentially slow. We propose a...

In recent literature, a new class of unbiased Monte Carlo estimators have been proposed, which is based on truncating a telescopic representation of the expectation of a functional of the stochastic process at an independent random level. The generality of the method lies in that it can...

Efficient inventory management in the face of product variety is an important part of retail operations management. In this paper, we analyze the optimal stocking policy for a retailer, in a setup with a single horizontally differentiated product with an arbitrary number of product variants,...

In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet possibly less liquid, exotic options, and a dynamic trading...

We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.