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We propose a new framework for modeling stochastic local volatility, with potential applications to modeling derivatives on interest rates, commodities, credit, equity, FX etc., as well as hybrid derivatives. Our model extends the…
We consider finite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the parameter uncertainty can sometimes…
The main purpose of this paper is to extend the information-based asset-pricing framework of Brody-Hughston-Macrina to a more general set-up. We include a wider class of models for market information and in contrast to the original paper,…
This paper studies convergence properties of optimal values and actions for discounted and average-cost Markov Decision Processes (MDPs) with weakly continuous transition probabilities and applies these properties to the stochastic…
In this paper, we consider a continuous-time Markov decision process (CTMDP) in Borel spaces, where the certainty equivalent with respect to the exponential utility of the total undiscounted cost is to be minimized. The cost rate is…
We present two methodologies on the estimation of rating transition probabilities within Markov and non-Markov frameworks. We first estimate a continuous-time Markov chain using discrete (missing) data and derive a simpler expression for…
A market with defaultable bonds where the bond dynamics is in a Heath-Jarrow-Morton setting and the forward rates are driven by an infinite number of Levy factors is considered. The setting includes rating migrations driven by a Markov…
In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model…
This paper studies function approximation for finite horizon discrete time Markov decision processes under certain convexity assumptions. Uniform convergence of these approximations on compact sets is proved under several sampling schemes…
Robust Markov Decision Processes (MDPs) are a powerful framework for modeling sequential decision-making problems with model uncertainty. This paper proposes the first first-order framework for solving robust MDPs. Our algorithm interleaves…
This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices…
We develop a novel deep learning approach for pricing European basket options written on assets that follow jump-diffusion dynamics. The option pricing problem is formulated as a partial integro-differential equation, which is approximated…
In this work, we study the problem of actively classifying the attributes of dynamical systems characterized as a finite set of Markov decision process (MDP) models. We are interested in finding strategies that actively interact with the…
In this paper, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic…
In the "positive interest" models of Flesaker-Hughston, the nominal discount bond system is determined by a one-parameter family of positive martingales. In the present paper we extend this analysis to include a variety of distributions for…
In this work we investigate an importance sampling approach for evaluating policies for a structurally time-varying factored Markov decision process (MDP), i.e. the policy's value is estimated with a high-probability confidence interval. In…
Motion planning under uncertainty for an autonomous system can be formulated as a Markov Decision Process with a continuous state space. In this paper, we propose a novel solution to this decision-theoretic planning problem that directly…
We develop a pricing model for Sovereign Contingent Convertible bonds (S-CoCo) with payment standstills triggered by a sovereign's Credit Default Swap (CDS) spread. We model CDS spread regime switching, which is prevalent during crises, as…
This paper aims to provide a simple modelling of speculative bubbles and derive some quantitative properties of its dynamical evolution. Starting from a description of individual speculative behaviours, we build and study a second order…
For additive actuator and sensor faults, we propose a systematic method to design a state-space fault estimation filter directly from Markov parameters identified from fault-free data. We address this problem by parameterizing a…