We consider a fractional version of the Heston volatility model which is inspired by [H. Guennoun et al., SIAM J. Financial Math,, 9 (2018), pp. 1017--1045]. Within this model we treat portfolio op...

In this paper, we investigate the representation of a class of non-Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular, the underlying process can be seen as a non-Gaussian extension of the Ornstein–Uhlenbeck process, hence generalizing the representation results of Muravlev, Russian Math. Surveys 66 (2), 2011 as well as Harms and Stefanovits, Stochastic Process. Appl. 129, 2019 to the non-Gaussian case.

We solve the problem of an investor who maximizes utility but faces random preferences. We propose a problem formulation based on expected certainty equivalents. We tackle the time‐consistency issues arising from that formulation by applying the equilibrium theory approach. To this end, we provide the proper definitions and prove a rigorous verification theorem. We complete the calculations for the cases of power and exponential utility. For power utility, we illustrate in a numerical example that the equilibrium stock proportion is independent of wealth, but decreasing in time, which we also supplement by a theoretical discussion. For exponential utility, the usual constant absolute risk aversion is replaced by its expectation.

The dynamic structure of electricity markets, where uncertainties abound due to, e.g., demand variations and renewable energy intermittency, poses challenges for market participants. We propose generative adversarial networks (GANs) to generate synthetic electricity price data. This approach aims to provide comprehensive data that accurately reflect the complexities of the actual electricity market by capturing its distribution. Consequently, we would like to equip market participants with a versatile tool for successfully dealing with strategy testing, risk model validation, and decision-making enhancement. Access to high-quality synthetic electricity price data is instrumental in cultivating a resilient and adaptive marketplace, ultimately contributing to a more knowledgeable and prepared electricity market community. In order to assess the performance of various types of GANs, we performed a numerical study on Turkey’s intraday electricity market weighted average price (IDM-WAP). As a key finding, we show that GANs can effectively generate realistic synthetic electricity prices. Furthermore, we reveal that the use of complex variants of GAN algorithms does not lead to a significant improvement in synthetic data quality. However, it requires a notable increase in computational costs.

It is generally understood that a given one-dimensional diffusion may be transformed by a Cameron–Martin–Girsanov measure change into another one-dimensional diffusion with the same volatility but a different drift. But to achieve this, we have to know that the change-of-measure local martingale that we write down is a true martingale. We provide a complete characterisation of when this happens. This enables us to discuss the absence of arbitrage in a generalised Heston model including the case where the Feller condition for the volatility process is violated.