Renewable resources are affected by both environmental variability, which makes the year-to-year stock growth uncertain, and the risk of irreversible events (e.g., a stock collapse). Little is known about how a renewable resource harvester would optimally respond to the combined effects of both...

Optimal simple rules for the monetary policy of the first stochastically dominant crypto-currency are derived in a Dynamic Stochastic General Equilibrium (DSGE) model, in order to provide optimal responses to changes in inflation, output, and other sources of uncertainty.The optimal monetary...

We study multidimensional Cram\'er-Lundberg risk processes where agents, located on a large sparse network, receive losses form their neighbors. To reduce the dimensionality of the problem, we introduce classification of agents according to an arbitrary countable set of types. The ruin of any...

We introduce the log-normal stochastic volatility (SV) model for the dynamics of a short interest rate in the Cheyette model. We assume non-zero correlation between the dynamics of the short rate and the log-normal SV driver for modelling positive implied volatility skews observed in...

This work introduces two new financial derivatives into the finance literature. The first is the Return Barrier Option, which has emerged recently as a popular contract in the OTC markets. This contract is similar to a barrier option, but the knock-out event depends on an asset's returns, rather...

In this paper, we focus on pricing and hedging of Guaranteed Minimum Benefits (GMBs) and we extend the existing framework by assuming the underlying asset dynamics evolve under a regime-switching jump-diffusion environment. Two basic GMB contracts, Guaranteed Minimum Maturity Benefit (GMMB) and...

We introduce the Newton--Sinkhorn and implied Newton algorithms which significantly speed up the Sinkhorn algorithm that [Guyon, The joint S&P 500/VIX smile calibration puzzle solved, Risk, April 2020] used to build the first arbitrage-free model exactly consistent with S&P 500 and VIX market...

The quintic Ornstein-Uhlenbeck volatility model is a stochastic volatility model where the volatility process is a polynomial function of degree five of a single Ornstein-Uhlenbeck process with fast mean reversion and large vol-of-vol. The model is able to achieve remarkable joint fits of the...

We calibrate neural stochastic differential equations jointly to S&P 500 smiles, VIX futures, and VIX smiles. Drifts and volatilities are modeled as neural networks. Minimizing a suitable loss allows us to fit market data for multiple S&P 500 and VIX maturities. A one-factor Markovian stochastic...

In this note we formulate an optimality problem for Stochastic process with a regime absorbing state. We present a solution for this problem as a pair of differential equations that are recusrsively linked. As an application I obtain an analytical for the Merton portfolio problem in a case for a...