In this paper we study a continuous time, optimal stochastic investment problem under limited resources in a market with N firms. The investment processes are subject to a time-dependent stochastic constraint. Rather than using a dynamic programming approach, we exploit the concavity of the...

A Hidden Markov Model (HMM) is used to model the VIX (the Cboe Volatility Index). A 4- state Gaussian mixture is fitted to the VIX price history from 1990 to 2022. Using a growing window of training data, the price of the S&P500 is predicted and two trading algorithms are presented, based on the...

We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting...

We derive closed form analytic formulas for European vanilla options in the driftless Oscillating Brownian Motion model defined by two semi-infinite regimes each with its own constant local volatility. In particular we solve the Ito and Stratonovich Fokker-Planck equations for the probability...

We explore buyback contracts in a supplier-retailer supply chain where the retailer faces a price-dependent downward-sloping demand curve subject to uncertainty. We formulate the problem as a supplier-led Stackelberg game and derive explicitly the equilibrium contract parameters along with the...

We extend the arithmetic multi-factor electricity spot price model proposed by Benth, Kallsen & Meyer-Brandis by adding stochastic mean-level processes to their model and by taking additional information on the future behavior of these mean-level processes into account. The available...

We develop a modelling framework for estimating and predicting weighted network data. The edge weights in weighted networks often arise from aggregating some individual relationships between the nodes. Motivated by this, we introduce a modelling framework for weighted networks based on the...

We propose a new stochastic volatility model for pricing options on assets that exhibit seasonal trends in volatility. Such assets are prevalent among commodities, with futures on grains and energy being an example. The model is based on the 3/2 stochastic volatility model, but includes a...

In this paper we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. This formula is useful for pricing and risk management as well as for extracting the implied volatility from...

We consider the Black and Scholes (1973) and Heston (1993) models and we generalize them to stochastic interest rates and maturity-dependent volatilities. In the Black-Scholes case we solve the extended model and provide a concrete form for the term structure of volatilities. In the Heston case...