Hirbod Assa

On Optimal Reinsurance Policy with Distortion Risk Measures and Premiums

In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the ceding company, the reinsurance company and the social planner can be formulated in the same way. Second, by introducing the “marginal indemnification functions”, we characterize the optimal reinsurance contracts. We show that, for an optimal policy, the associated marginal indemnification function only takes the values zero and one. We will see how the roles of the market preferences and premiums and that of the total risk are separated.

Hedging, Pareto Optimality, and Good Deals

In this paper, we will describe a framework that allows us to connect the problem of hedging a portfolio in finance to the existence of Pareto optimal allocations in economics. We will show that the solvability of both problems is equivalent to the No Good Deals assumption. We will then analyze the case of co-monotone additive monetary utility functions and risk measures.

Financial engineering in pricing agricultural derivatives based on demand and volatility

Purpose - – The purpose of this paper is twofold. First, the author proposes a financial engineering framework to model commodity prices based on market demand processes and demand functions. This framework explains the relation between demand, volatility and the leverage effect of commodities. It is also shown how the proposed framework can be used to price derivatives on commodity prices. Second, the author estimates the model parameters for agricultural commodities and discuss the implications of the results on derivative prices. In particular, the author see how leverage effect (or inverse leverage effect) is related to market demand. Design/methodology/approach - – This paper uses a power demand function along with the Cox, Ingersoll and Ross mean-reverting process to find the price process of commodities. Then by using the Ito theorem the constant elastic volatility (CEV) model is derived for the market prices. The partial differential equation that the dynamics of derivative prices satisfy is found and, by the Feynman-Kac theorem, the market derivative prices are provided within a Monte-Carlo simulation framework. Finally, by using a maximum likelihood estimator, the parameters of the CEV model for the agricultural commodity prices are found. Findings - – The results of this paper show that derivative prices on commodities are heavily affected by the elasticity of volatility and, consequently, by market demand elasticity. The empirical results show that different groups of agricultural commodities have different values of demand and volatility elasticity. Practical implications - – The results of this paper can be used by practitioners to price derivatives on commodity prices and by insurance companies to better price insurance contracts. As in many countries agricultural insurances are subsidised by the government, the results of this paper are useful for setting more efficient policies. Originality/value - – Approaches that use the methodology of financial engineering to model agricultural prices and compute the derivative prices are rather new within the literature and still need to be developed for further applications.

Modelling and pricing of catastrophe risk bonds with a temperature-based agricultural application

Catastrophe risk bonds are always within a multi-asset class portfolio of alternative risk premia in many hedge funds. In this paper, we consider an over-the-counter insurance contract on catastrophe risk between an insurance company and a hedge-fund. The contract acts as a bond within which the insurance company, which issues the bond, pays payments higher than the market risk-free interest, in order to be insured against the risk of a predefined natural catastrophe. The contract is priced by the utility indifference pricing method. We apply our framework to price agricultural catastrophe bonds in two cities in Iran where their harvests are exposed to the risk of low temperature.

Joint Games and Compatibility

Abstract We introduce the concepts of joint games and compatibility. In a joint game, members of the grand coalition have the option to split and participate in different underlying games, thereby maximizing their total worths. In order to determine whether the grand coalition will remain intact, we introduce the notion of compatibility of these games. A set of games is compatible if the core of the joint game is non-empty. We find a necessary and sufficient condition for compatibility.

Risk management under a prudential policy

In this paper, we study the structure of optimal contracts in banking system when there is no risk of moral hazard. We consider a risk management problem under a policy that reduces the excessive risk-taking behavior by making all banks bear part of the risk that they transfer to other parties in the market. First, we characterize the optimal solutions to the risk management problem, and, second, we find a necessary and sufficient condition under which the “risk of the tail events” will not be transferred. In particular, we will study the problem using two known risk measures, value at risk and conditional value at risk, and will show that in these cases, the optimal solutions are in the form of stop-loss policies. Copyright Springer-Verlag Italia 2015

A financial engineering approach to pricing agricultural insurances

Purpose - – The purpose of this paper is to introduce a continuous time version of the speculative storage model of Deaton and Laroque (1992) and to use for pricing derivatives, in particular insurances on agricultural prices. Design/methodology/approach - – The methodology of financial engineering is used in order to find the partial differential equations that the dynamics of derivative prices have to satisfy. Furthermore, by using the Monte-Carlo method (and Feynman-Kac theorem) the insurance prices is computed. Findings - – Results of this paper show that insurance prices (and derivative prices in general) are heavily influenced by market structure, in particular, the demand function specifications. Furthermore, through an empirical analysis, the performance of the continuous time speculative storage model is compared with the geometric Brownian motion model. It is shown that the speculative storage model outperforms the actual data. Practical implications - – Since the agricultural insurances in many countries are subsidised by government, the results of this paper can be used by policy makers to measure changes in agricultural insurance premiums in scenarios that market experiences changes in demand. In the same manner, insurance companies and investors can use the results of this paper to better price agricultural derivatives. Originality/value - – The issue of agricultural insurance pricing (in general derivative pricing) is of great concern to policy makers, investors and insurance companies. To the author’s knowledge, an approach which uses the methodology of financial engineering to compute the insurance prices (in general derivatives) is new within the literature.

Designing sound deposit insurances

Abstract Deposit insurances were blamed for encouraging the excessive risk taking behavior during the 2008 financial crisis. The main reason for this destructive behavior was “moral hazard risk”, usually caused by inappropriate insurance policies. While this concept is known and well-studied for ordinary insurance contracts, yet needs to be further studied for insurances on financial positions. In this paper, we set up a simple theoretical framework for a bank that buys an insurance policy to protect its position against market losses. The main objective is to find the optimal insurance contract that does not produce the risk of moral hazard, while keeping the bank’s position solvent. In a general setup we observe that an optimal policy is a multi-layer policy. In particular, we obtain a close form solution for the optimal insurance contracts when a bank measures its risk by either Value at Risk or Conditional Value at Risk. We show the optimal solutions for these two cases are two-layer policies.

Representation and approximation of convex dynamic risk measures with respect to strong–weak topologies

ABSTRACT We provide a representation for strong-weak continuous dynamic risk measures from Lp into Lpt spaces where these spaces are equipped respectively with strong and weak topologies and p is a finite number strictly larger than one. Conversely, we show that any such representation that admits a compact (with respect to the product of weak topologies) sub-differential generates a dynamic risk measure that is strong--weak continuous. Furthermore, we investigate sufficient conditions on the sub-differential for which the essential supremum of the representation is attained. Finally, the main purpose is to show that any convex dynamic risk measure that is strong-weak continuous can be approximated by a sequence of convex dynamic risk measures which are strong--weak continuous and admit compact sub-differentials with respect to the product of weak topologies. Throughout the arguments, no conditional translation invariance or monotonicity assumptions are applied.

Reinsurance Optimal Design with Distortion Risk Measures and Risk Premiums

In this paper we consider the problem of optimal reinsurance design for general distortion risk measures and premiums. In the first part of the paper, we find the Lagrangian dual of the primal optimal reinsurance problem and show the strong duality holds. Therefore we characterize the optimal reinsurance policies by solving the dual problem and we will see that the solutions always have a multilayer structure. In addition we will see that for particular risk measures VaR and CVaR the optimal solutions are stop-loss policies. In the second part we focus our attention to reinsurance policies that are usually traded in the market, namely stop-loss, stop-loss after quota share and quota-share after stop-loss. We show how by one can find the optimal retentions by checking Karush-Kuhn-Tucker conditions. At the end, we study the particular cases VaR or CVaR.