We consider an asset allocation problem in a continuous-time model with stochastic volatility and (possibly correlated) jumps in both, the asset price and its volatility. First, we derive the optimal portfolio for an investor with constant relative risk aversion. One main finding is that the demand for jump risk now also includes a hedging component, which is not present in models without jumps...

This paper examines jump dynamic patterns in three Chinese medical stocks. It also compares the Value-at-Risk (VaR) forecasting performance of a newly proposed realized volatility model allowing for jumps with that of two commonly used realized volatility models, which do not account for jumps. Using the Heterogeneous Autoregressive Realized Volatility model that allows for jumps (HAR-CJN), we ...

Market microstructure theories suggest that the durations between transactions carry information about volatility. This paper puts forward a model featuring stochastic volatility, stochastic conditional duration, and jumps to analyze high frequency returns and durations. Durations affect price jumps in two ways: as exogenous sampling intervals, and through the interaction with volatility. We ad...

In this paper, using an algorithm based on retrospective rejection sampling scheme introduced in [2, 6], we propose an exact simulation of a Brownian diffusion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps, providing numerical simulations. Our main contribution is to manage the technical difficulty due to the presence of two jumps thanks to a new ex...

In this paper, we address stability and robustness properties of hybrid limit cycles for a class of hybrid systems with multiple jumps in one period. The main results entail equivalent characterizations of stability of hybrid limit cycles for hybrid systems. The hybrid limit cycles may have multiple jumps in one period and the jumps are allowed to occur on sets. Conditions guaranteeing robustne...

We extend the Yamada-Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps, in the special case where small jumps are summable.

In this paper we study a general stochastic fluid model with a single infinite capacity buffer, where the buffer content can change continuously as well as by instantaneous upward jumps. The continuous as well as the instantaneous change is modulated by an external environment process modelled as a finite state continuous time Markov chain. The Laplace-Stieltjes transform of the steady-state jo...

Realized volatility of stock returns is often decomposed into two distinct components that are attributed to continuous price variation and jumps. This paper proposes a tobit multivariate factor model for the jumps coupled with a standard multivariate factor model for the continuous sample path to jointly forecast volatility in three Chinese Mainland stocks. Out of sample forecast analysis show...

In a fundamental test of quantum mechanics, we have observed 228 000 quantum jumps of a single trapped and laser cooled Sr ion. This represents a statistical increase of two orders of magnitude over previous similar analyses of quantum jumps. Compared to other searches for nonrandomness in quantum mechanical processes, using quantum jumps simplifies the interpretation of data by eliminated mult...

Substantial evidence from animal studies indicates that jumping increases bone mass and strength. However, most studies have focused on the take-off, rather than the landing phase of jumps. Thus, we compared the effects of landing and upward jump impact on trabecular bone mass and microarchitecture. Male Wistar rats aged 10 weeks were randomly assigned to the following groups: sedentary control...