We propose a new variational approximation of the joint posterior distribution of the log-volatility in the context of large Bayesian VARs. In contrast to existing approaches that are based on local approximations, the new proposal provides a global approximation that takes into account the...

The fundamental connection between stochastic differential equations (SDEs) and partial differential equations (PDEs) has found numerous applications in diverse fields. We explore a similar link between stochastic calculus and combinatorial PDEs on graphs with Hodge structure, by showing that...

We use a novel definition of tail risk for option pricing purposes, based on the concept of almost stochastic dominance (ASD) in order to examine empirical “puzzles” documented in several high profile studies of the market for S&P 500 index options. We find that with one exception these...

We define two new stochastic orders combining probability ratio and likelihood ratio and specify two respective classes of payoff functions, which nest most models in the literature as special cases, such that a risk change satisfies one of the two stochastic orders if and only if given any...

We show how the classical Lagrangian approach to solving constrained optimization problems from standard calculus can be extended to solve continuous time stochastic optimal control problem. Connections to mainstream approaches such as the Hamilton-Jacobi-Bellman equation and the stochastic...

This work aims to demonstrate how a trifactorial stochastic model, which we call CIR3, can be turned into a forecasting tool to predict changes in the industrial production of electric and gas utilities. The model accounts for several stylized facts such as the mean reversion of both the process...

In this paper, we propose a new approach for stochastic control problems arising from utility maximization. The main idea is to directly start from the dynamical programming equation and compute the conditional expectation using a novel representation of the conditional density function through...

We propose a new methodology for pricing options on flow forwards by applying infinite-dimensional neural networks. We recast the pricing problem as an optimization problem in a Hilbert space of real-valued function on the positive real line, which is the state space for the term structure...

This research proposes a new option pricing model. The model revises the unimodal probability distribution assumption used in the past, and proposes a bimodal probability distribution for option pricing. The bimodal probability distribution proposed in this study can be degenerated to a unimodal...

We study scheduling in a stochastic processing network where there are multiple job types, multiple homogeneous servers, and jobs are expressed as directed acyclic graphs (DAGs) of tasks. Our main motivation is the scheduling of cloud computing resources where customers express their requests as...