After analyzing the uncertainty of technology innovation diffusion (TID), this paper proposes the model of enterprises’ TID based on geometric Brownian motion with jump, and analyzes the optional timing and influence of adopting innovation technology on TID by each parameter. The results show that enterprise should immediately adopts the technology when its market demand is greater than the opt...

The paper studies the benchmark approach for pricing and hedging in incomplete markets where the investor has to filter the incomplete information. We consider a jump diffusion Markov modulated market model and derive the growth optimal portfolio (GOP), by using the stochastic control method. Using GOP, we price and hedge European options where the existence of the equivalent martingale measure...

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 ...

In order to price commodity derivatives, it is necessary to estimate the market prices of risk as well as the functions of the stochastic processes of the factors in the model. However, the estimation of the market prices of risk is an open question in the jump-diffusion derivative literature when a closed-form solution is not known. In this paper, we propose a novel approach for estimating the...

In this paper, we propose a modified Lévy jump diffusion model with market sentiment memory for stock prices, where the market sentiment comes from data mining implementation using Tweets on Twitter. We take the market sentiment process, which has memory, as the signal of Lévy jumps in the stock price. An online learning and optimization algorithm with the Unscented Kalman filter (UKF) is then ...

In this paper we propose a jump-diffusion type model which recovers the main characteristics of electricity spot price dynamics in the Nordic market, including seasonality, mean-reversion and spiky behavior. We show how the calibration of the market price of risk to actively traded futures contracts allows for efficient valuation of Nord Pool's Asian-style options written on the spot electricit...

In this paper, we consider the problem of mean-variance hedging in an incomplete market where the underlying assets are jump diffusion processes which are driven by Brownian motion and doubly stochastic Poisson processes. This problem is formulated as a stochastic control problem and closed form expressions for the optimal hedging policy are obtained using methods from stochastic control and th...

Many examples of complex systems are provided by applications in finance and economics areas. Some of intrinsic features of such systems lie with the fact that their parts are interacting in a non-trivial dynamic manner and they can be subject to stochastic forces and jumps. The mathematical models for such systems are often based on stochastic differential equations and efficient computational...

We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markovswitching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic progr...