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The sub-fractional Brownian motion (sfBm) is a stochastic process, characterized by non-stationarity in their increments and long-range dependency, considered as an intermediate step between the standard Brownian motion (Bm) and the…
We propose a general two-period model where electrical vehicles (EVs) can reserve charging sessions in the day-ahead market and swap them in the real-time market. Under the model, we explore several candidate mechanisms for running the two…
This paper studies pricing derivatives in an age-dependent semi-Markov modulated market. We consider a financial market where the asset price dynamics follow a regime switching geometric Brownian motion model in which the coefficients…
Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.
We study a stochastic control approach to managed futures portfolios. Building on the Schwartz 97 stochastic convenience yield model for commodity prices, we formulate a utility maximization problem for dynamically trading a single-maturity…
We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift,…
The accurate prediction of short-term electricity prices is vital for effective trading strategies, power plant scheduling, profit maximisation and efficient system operation. However, uncertainties in supply and demand make such…
Electricity price forecasting has become a critical tool for decision-making in energy markets, particularly as the increasing penetration of renewable energy introduces greater volatility and uncertainty. Historically, research in this…
The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a…
This paper compares the optimal investment problems based on monotone mean-variance (MMV) and mean-variance (MV) preferences in the L\'{e}vy market with an untradable stochastic factor. It is an open question proposed by Trybu{\l}a and…
We presented a methodology to approximate the entropy production for Brownian motion in a tilted periodic potential. The approximation stems from the well known thermodynamic uncertainty relation. By applying a virial-like expansion, we…
In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation…
This paper considers the valuation of a European call option under the Heston stochastic volatility model. We present the asymptotic solution to the option pricing problem in powers of the volatility of variance. Then we introduce the…
Real-Time Bidding (RTB) is an important mechanism in modern online advertising systems. Advertisers employ bidding strategies in RTB to optimize their advertising effects subject to various financial requirements, especially the…
With the rapid growth of electric vehicles (EVs), EV aggregators have been playing a increasingly vital role in power systems by not merely providing charging management but also participating in wholesale electricity markets. This work…
To enable the participation of stochastic distributed energy resources in ancillary service markets, the Danish transmission system operator, Energinet, mandates that flexibility providers satisfy a minimum 90% reliability requirement for…
The rapid growth of weather-dependent renewable generation increases price volatility and imbalance penalty risk in power markets, creating the need for advanced quantitative trading strategies. We develop a data-driven continuous-time…
Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…
We propose a novel algorithm which allows to sample paths from an underlying price process in a local volatility model and to achieve a substantial variance reduction when pricing exotic options. The new algorithm relies on the construction…
We consider a large market model of defaultable assets in which the asset price processes are modelled as Heston-type stochastic volatility models with default upon hitting a lower boundary. We assume that both the asset prices and their…