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Markovian-regime-switching (MRS) models are commonly used for modelling economic time series, including electricity prices where independent regime models are used, since they can more accurately and succinctly capture electricity price…
In this paper, we propose a minimal model beyond geometric Brownian motion that aims to describe price actions with market inefficiency. From simple financial theory considerations, we arrive at a simple two-variable hidden Markovian time…
We introduce the notion of relative volatility/intermittency and demonstrate how relative volatility statistics can be used to estimate consistently the temporal variation of volatility/intermittency when the data of interest are generated…
We consider an optimal control problem, where a Brownian motion with drift is sequentially observed, and the sign of the drift coefficient changes at jump times of a symmetric two-state Markov process. The Markov process itself is not…
We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their…
In this study, we consider the asset pricing under model uncertainty with discrete time and states structure. For the single-period securities model, we give a novel definition of arbitrage under a family of probability, and explore of its…
Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$ of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ a one-dimensional positive diffusion process independent of the Brownian motion $B$. For both the…
We consider a financial market model driven by an R^n-valued Gaussian process with stationary increments which is different from Brownian motion. This driving noise process consists of $n$ independent components, and each component has…
In this article we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market…
We derive a closed-form expression capturing the degree of Relative Risk Aversion (RRA) of investors for non-"fair" lotteries. We argue that our formula is superior to earlier methods that have been proposed, as it is a function of only…
This paper presents an optimal allocation problem in a financial market with one risk-free and one risky asset, when the market is driven by a stochastic market price of risk. We solve the problem in continuous time, for an investor with a…
We develop an exactly-solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations we obtain the steady-state probabilities. Generally…
Derivatives, as a critical class of financial instruments, isolate and trade the price attributes of risk assets such as stocks, commodities, and indices, aiding risk management and enhancing market efficiency. However, traditional hedging…
Optimal liquidation of an asset with unknown constant drift and stochastic regime-switching volatility is studied. The uncertainty about the drift is represented by an arbitrary probability distribution; the stochastic volatility is…
We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in…
This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements:…
In this paper, we consider a num\'eraire-based utility maximization problem under constant proportional transaction costs and random endowment. Assuming that the agent cannot short sell assets and is endowed with a strictly positive…
Let $\{B(t), t\ge 0\}$ be a Brownian motion. Consider the Brownian motion risk model with interest rate collection and tax payment defined by \begin{align}\label{Rudef}…
We develop an arbitrage-free random field LIBOR market model to price cross-currency derivatives. The uncertainty of the forward LIBOR rates of our cross-currency model is driven by a two time parameter random field instead of a finite…
Pricing derivatives goes back to the acclaimed Black and Scholes model. However, such a modeling approach is known not to be able to reproduce some of the financial stylized facts, including the dynamics of volatility. In the mathematical…