Hirbod Assa

In the realm of portfolio management, the focus lies on constructing a well-diversified portfolio to mitigate unsystematic risk, allowing for the identification and measurement of systematic risk e.g. through uni-factor models, such as CAPM, and multi-factor models, such as APT. This approach is rooted in the belief that, with a sufficiently diversified portfolio, unsystematic risk in theory can be eliminated, making the remaining systematic risk more apparent. While diversification is the means to diversify the unsystematic risk in a portfolio management problem, pooling strategies, with a limited strategy of just expanding the pool members, necessitate a distinct approach to systematic risk. In such scenarios, the challenge lies in disentangling the impact of systematic factors from idiosyncratic influences within a pool. This paper explores the methodologies and considerations unique to pooling situations, shedding light on the complexities involved in identifying and quantifying systematic risk in a pool. In our effort to assess the concept of systematic risk in a pool, we adopt an approach that identifies the defining characteristics of systematic risks, which remain invariant regardless of the number of losses or any manipulations within a finite set of losses. To explore these principles, we find a framework of risk management on sequences in Banach lattices to be particularly suitable. In establishing these principles, we introduce the notion of “systematic compatibility”, signifying invariance to variations in finite changes within a sequence of losses. Consequently, we observe that while systematic risk often possesses an implicit representation in the risk space, it exhibits an explicit representation in the bi-dual space. Moreover, we introduce systematic compatible risk measures and establish their dual characterization. We demonstrate that risk measurement can naturally be represented as a split into a summation of systematic and unsystematic components. In practical applications, we employ these measures to address risk management problems, with a specific emphasis on risk pooling scenarios. In revisiting the traditional “principle of insurance” (POI), we propose an extension called the “principle of pooling” (POP). By showing that the principle of pooling holds if and only if the systematic risk is secure, we investigate this novel concept.

The Value-at-Risk (VaR) and the Expected Shortfall (ES) are the two most popular risk measures in banking and insurance regulation. To bridge between the two regulatory risk measures, the Probability Equivalent Level of VaR-ES (PELVE) was recently proposed to convert a level of VaR to that of ES. It is straightforward to compute the value of PELVE for a given distribution model. In this paper, we study the converse problem of PELVE calibration, that is, to find a distribution model that yields a given PELVE, which may either be obtained from data or from expert opinion. We discuss separately the cases when one-point, two-point, n-point and curve constraints are given. In the most complicated case of a curve constraint, we convert the calibration problem to that of an advanced differential equation. We apply the model calibration techniques to estimation and simulation for datasets used in insurance. We further study some technical properties of PELVE by offering a few new results on monotonicity and convergence.

The COVID-19 pandemic caused a significant disruption to food demand, leading to changes in household expenditure and consumption patterns. This paper presents a method for analyzing the impact of such demand shocks on a producer’s decision to sell a commodity during economic turmoil. The method uses an artificial neural network (ANN) to approximate the optimal value function for a general stochastic differential equation and calculate the partial derivatives of the value function with respect to various parameters of both the diffusion process and the payoff function. This approach allows for sensitivity analysis of the optimal stopping problem and can be applied to a range of situations beyond just the COVID-19 crisis.

Calibration of multidimensional economic problems proven to be difficult, as there is a high risk of problem miss-identification. In this paper we propose a multi-stage calibration method to estimate the six parameters of a commodity market price model that includes storage. We assume that the commodity prices are derived from the optimal commodity storage time when the demand process follows a mean-reverting log-Ornstein–Uhlenbeck process. Using two alternative value functions, first we propose a two-stage method to maximize the likelihood functions obtained by Milstein method. Then by considering a regularized likelihood functions we propose a multi-stage method to calibrate the parameters of our problem. After we realize our method is perfectly performing on the simulated data, we encounter it to actual data and calibrate the parameters. We observe that our multi-stage calibration method is robust and that the storage model outperforms the non-storage model.

Motivated by macroeconomic risks, such as the COVID-19 pandemic, we consider different risk management setups and study efficient insurance schemes in the presence of low probability shock events that trigger losses for all participants. More precisely, we consider three platforms: the risk-sharing, insurance and market platform. First, we show that under a non-discriminatory insurance assumption, it is optimal for everybody to equally share all risk in the market. This gives rise to a new concept of a contingent premium which collects the premia ex-post after the losses are realised. Insurance is then a mechanism to redistribute wealth, and we call this a risk-sharing solution. Second, we show that in an insurance platform, where the insurance is regulated, the tail events are not shared, but borne by the government. Third, in a competitive market we see how a classical solution can raise the risk of insolvency. Moreover, in a decentralised market, the equilibrium cannot be reached if there is adequate sensitivity to the common shock events. In addition, we have applied our theory to a case where the losses are calibrated based on the UK Coronavirus Job Retention Scheme.

In this article, we introduce price index insurances on agricultural goods. Although these seem similar to derivatives, there are significant differences between price index insurances and derivatives. First, unlike derivatives, there are no entrance barriers for purchasing insurances, making them the risk management tools that are accessible to almost all farmers. Second, since insurances are issued in a certain number for any individual farm, unlike futures, for example, they cannot be used for speculation and are used solely for hedging price risk. Third, unlike forwards, they are heavily regulated and do not default and cause counterparty risk. In addition to all differences (or benefits), such products have just recently been introduced in the agricultural insurance market. In this article, we investigate if there could have been a financially viable market where these products are traded. More precisely, we investigate whether an insurance company can design a portfolio of optimal contracts that gives a higher Sharpe ratio than the financial market index prices (here, FTSE 100 and other three major indexes). To reach the article’s objective, we take three steps, in considering theoretical, practical, and corporation standpoints. In the first step, we show what an optimal contract would look like from the demand side in a theoretical setup and we obtain the optimal contract from the farmers' standpoint. In the second step, by adopting a more practical approach in meeting the Key Performance Indicators requirements set by the market participants (both demand and supply side), we find the optimal policies specifications from the first step, in the market equilibrium. This step also helps to determine some unobservable market parameters like volatility. Finally, by adopting a corporation standpoint we bring our model to the U.K. farm index prices and find an optimal portfolio of the products on products from 10 commodities. We demonstrate that investing in such a business is financially viable, as the optimal insurance portfolio produces a Sharpe ratio that outperforms the FTSE 100 and other major market indexes.