2 Abstract Correlated defaults have been an important area of research in credit risk analysis with the advent of a basket of credit derivatives. Even the simple credit derivatives should be considered a basket of two default risks since the bankruptcy risk of the derivative issuer is also a factor. Considering jumps in the asset value helps to model the surprise risk of default in a group of f...

This paper is a further extension of the method proposed in Itkin (2014) as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is applied to these PIDEs. To solve the diffusion equation we use standard fini...

Fast pricing of American-style options has been a difficult problem since it was first introduced to the financial markets in 1970s, especially when the underlying stocks’ prices follow some jump-diffusion processes. In this paper, we extend the “true martingale algorithm” proposed by Belomestny et al. (2009) for the pure-diffusion models to the jump-diffusion models, to fast compute true tight...

We consider the hedging problem in a jump-diffusion market with correlated assets. For this purpose, we employ the locally risk-minimizing approach and obtain the hedging portfolio as a solution of a multidimensional system of linear equations. ‎This system shows that in a continuous market, independence and correlation assumptions of assets lead to the same locally risk-minimizing portfolio. ‎...

We develop the process of discounting when underlying rates follow a jump-diffusion process, that is, when, in addition to diffusive behavior, suffer series finite discontinuities located at random Poissonian times. Jump amplitudes are also and governed by an arbitrary density. Such model may describe economic evolution, specially extreme situations occur (pandemics, global wars, etc.). When, b...

We investigate a continuous-time version of the mean-variance portfolio selection model with jumps under regime switching. The portfolio selection is proposed and analyzed for a market consisting of one bank account andmultiple stocks. The random regime switching is assumed to be independent of the underlying Brownian motion and jump processes. A Markov chain modulated diffusion formulation is ...

The purpose of this paper is to derive the stochastic expansion of self-normalized-residual functionals stemming from a class of diffusion type processes observed at high frequency, where total observing period may or may not tend to infinity. The result enables us to construct some explicit statistics for goodness of fit tests, consistent against “presence of a jump component” and “diffusion-c...

We derive the stochastic master equations which describe the evolution of open quantum systems in contact with a heat bath and undergoing indirect measurements. These equations are obtained as a limit of a quantum repeated measurement model where we consider a small system in contact with an infinite chain at positive temperature. At zero temperature it is well-known that one obtains stochastic...

Scaling limits of continuous time random walks are used in physics to model anomalous diffusion, in which a cloud of particles spreads at a different rate than the classical Brownian motion. Governing equations for these limit processes generalize the classical diffusion equation. In this article, we characterize scaling limits in the case where the particle jump sizes and the waiting time betw...