We reduce the problem of pricing continuously monitored defaultable securities (namely, barrier type options, corporate debts) under a stochastic interest rate framework to calculations of boundary crossing probabilities (BCP) for Brownian Motion (BM) with stochastic boundaries. For the case...

The climate rescue is on the top of many agendas. In this context, emission trading schemes are considered as promising tools. The regulatory framework of an emission trading scheme introduces a market for emission allowances and creates need for risk management by appropriate financial...

Tackling climate change is at the top of many agendas. In this context, emission trading schemes are considered as promising tools. The regulatory framework for an emission trading scheme introduces a market for emission allowances and creates a need for risk management by appropriate financial...

Using the martingale approach we find sufficient conditions for exponential boundedness of first passage times over a level for ergodic first order autoregressive sequences (AR(1)). Further, we prove a martingale identity and use it for obtaining explicit bounds for the expectation of exit times.

We study a piece-wise deterministic Markov process having jumps of i.i.d. sizes with a constant intensity and decaying at a constant rate (a special case of a storage process with a general release rule). Necessary and sufficient conditions for the process to be ergodic are found, its stationary...

A firm-value model similar to the one proposed by Black and Cox (1976) is considered. Instead of assuming a constant and known default boundary, the default boundary is an unobserved stochastic process. This process has a Brownian component, reflecting the influence of uncertain effects on the...

We extend some known results on a relation between the distribution tails of the continuous local martingale supremum and its quadratic variation to the case of locally square integrable martingale with bounded jumps. The predictable and optional quadratic variations are involved in the main result.

We give explicit upper bounds for convergence rates when approximating (both one- and two-sided general curvlinear) boundary crossing probabilities for the Wiener process by similar probabilities for close boundaries (of simpler form for which computing the possibility is feasible). In...

We discuss a solution of the optimal stopping problem for the case when a reward function is a power function of a process with independent stationary increments (random walks or Levy processes) on an infinite time interval. It is shown that an optimal stopping time is the first crossing time...

Solving some integro-differential equation we find the Laplace transformation of the first passage time for Filtered Poisson Process generated by pulses with uniform or exponential distributions. Also, the martingale technique is applied for approximations of expectations accuracy is veryfying...