Before making purchase decisions, consumers often search for information on product attributes.In this paper, we incorporate a key feature of consumer search behavior---namely, search intensity---into a stochastic dynamic model. Specifically, motivated by industry evidence, we model search...

We consider an insurance market consisting of multiple competitive insures with a mean filed interaction via their terminal wealths under the exponential performance. It is assumed that each insurer regulates her risk by controlling the number of polices. We respectively establish the constant...

This paper introduces dynamic models for the spot foreign exchange rate with capturing both the rare events and the time-inhomogeneity in the fluctuating currency market. For the rare events, we use a compound Poisson process with log-normal jump amplitude to describe the jumps. As for the...

In this paper, we investigate a sequential maximum likelihood estimator of the unknown drift parameter for a class of reflected generalized Ornstein–Uhlenbeck processes driven by spectrally positive Lévy processes. In both of the cases of negative drift and positive drift, we prove that the...

In this paper, we consider a general Lévy risk model with two-sided jumps and a constant dividend barrier. We connect the ruin problem of the ex-dividend risk process with the first passage problem of the Lévy process reflected at its running maximum. We prove that if the positive jumps of the...

In this paper, we study the term structures of interest rates and foreign exchange rates through establishing a state-price deflator. The state-price deflator considered here can be viewed as an extension to the potential representation of the state-price density in [Rogers, L.C.G., 1997. The...

In this note, we investigate the existence of a weak mild solution to a stochastic interacting model (described by a system of stochastic partial differential equations) with stepping-stone noises by adopting a weak convergence argument.