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...

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...

This paper proposes a novel approach for pricing discretely monitored multi-asset barrier options and computing joint survival probability in multivariate exponential Levy asset price models. We calculate the Fourier transform of appropriately dampened value functions recursively using...

We develop a data-driven approach for options market making. Using stock options data from CBOE, we find that both buy and sell orders exhibit strong self-excitation but insignificant cross-excitation. We show that a Hawkes process with a time-varying baseline intensity and the power law kernel...

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...

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...

We develop a novel deep learning method for the enhanced index tracking problem, which aims to outperform an index while effectively controlling the tracking error. We generate a dynamic trading policy from a neural network that accepts a set of features as input. We design four blocks in the...