Polynomial affine approach to HARA utility maximization with applications to OrnsteinUhlenbeck 4/2 models.

Optimal market completion through financial derivatives with applications to volatility risk

“…represents the 1 norm of allocations at time t. Note that this objective is equivalent to maximizing the cash position while shorting less. Escobar-Anel et al (2022) demonstrated that the redundancy offers no additional help with either the investor's expected utility or their risky asset exposure in the case of two one-factor assets. In the next proposition, we demonstrate a generalized conclusion, which applies to any diffusion model.…”

“…an infinite number of strategies, each linked to a choice of derivative, producing the same maximum expected utility). The problem of infinitely many solutions and the optimal choice of derivatives was studied in the recent paper Escobar-Anel et al (2022) in the context of the Black-Scholes-Merton model. The paper proposed an optimization criterion (i.e.…”

“…This method was later named the BGSS and Cong and Oosterlee (2017) utilized the stochastic grid bundling method for conditional expectation estimation, introduced in Jain and Oosterlee (2015), further enhancing the accuracy of BGSS. Additionally, Zhu and Escobar-Anel (2022) targeted unsolvable continuous-time models, proposing an efficient and accurate simulation-based method, namely the polynomial affine method for constant relative risk aversion utility (PAMC). The second hurdle appears in the complexity of derivatives' price dynamics which, in contrast to traditional asset classes, could lead to highly non-linear stochastic differential equations.…”

“…The multitude of financial derivatives available in the market offers investors non-unique optimal choice in terms of expected utility theory (EUT) maximization. Hence we extend the additional optimization criterion proposed in Escobar-Anel et al (2022), namely risk exposure minimization, from the family of GBM to SV models. This aids investors with practical derivative selection in a popular stock markets modeling setting.…”

“…We build upon the double optimization approach (i.e. expected utility maximization and risk exposure minimization) proposed in Escobar-Anel et al (2022); demonstrating that strangle options are the best choices for market completion within equity options. Furthermore, we explore the benefit of using volatility index derivatives and conclude that they could be more convenient substitutes when only longterm maturity equity options are available.…”