Mijatovic and Pistorius (Math. Finance, 2013) proposed an efficient Markov chain approximation method for pricing European and barrier options in general one-dimensional Markovian models. However, sharp convergence rates of this method for realistic financial payoffs, which are non-smooth, are...

Continuous time Markov chain (CTMC) approximation is an intuitive and powerful method for pricing options in general Markovian models. This paper analyzes how grid design affects the convergence behavior of barrier and European options in general diffusion models. Using the spectral method, we...

The drawdown in the price of an asset shows how much the price falls relative to its historical maximum. This paper considers the pricing problem of American style drawdown call options, which allow the holder to optimally choose the time to receive a call payoff written on the drawdown. Our...

We solve the quadratic hedging problem by deep learning in discrete time. We consider three deep learning algorithms corresponding to three architectures of neural network approximation: approximating controls of different periods by different feedforward neural networks (FNNs) as proposed by...

We propose an efficient computational method based on continuous-time Markov chain (CTMC) approximation to compute the distributions of the speed and duration of drawdown for general one-dimensional (1D) time-homogeneous Markov processes. We derive linear systems for the Laplace transforms of...

We propose a reinforcement learning (RL) approach to solve the continuous-time mean-variance portfolio selection problem in a regime-switching market, where the market regime is unobservable. To encourage exploration for learning, we formulate an exploratory stochastic control problem with an...

Motivated by the need to model time-dependent behavior, this paper studies additive subordination, which we show is a useful technique for constructing time-inhomogeneous Markov processes with analytical tractability. This technique is a natural generalization of Bochner's subordination, which...

Distance to default (DTD) is a strong predictor of default risk derived from structural models. This paper specifies a stressed version of DTD ("stressed DTD'') to measure time-varying corporate default risk in the event that a systematic stress scenario occurs. Compared with the ordinary DTD,...

The Basic Affine Jump Diffusion (BAJD) process is widely used in financial modeling. In this paper, we develop an exact analytical representation for its transition density in terms of a series expansion that is uniformly-absolutely convergent on compacts. Computationally, our formula...