We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator....

We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator....

This paper develops an eigenfunction expansion approach to solve discretely monitored first passage time problems for a rich class of Markov processes, including diffusions and subordinate diffusions with jumps, whose transition or Feynman-Kac semigroups possess eigenfunction expansions in L2...

This paper studies subordinate Ornstein-Uhlenbeck (OU) processes, i.e., OU diffusions time changed by L\'{e}vy subordinators. We construct their sample path decomposition, show that they possess mean-reverting jumps, study their equivalent measure transformations, and the spectral representation...

This paper proposes a new approach to solve finite-horizon optimal stopping problems for a class of Markov processes that includes one-dimensional diffusions, birth-and-death (BD) processes, and jump-diffusions and continuous-time Markov chains obtained by time changing diffusions and BD...

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 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...

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...