Ramin Okhrati

Hedging of defaultable claims in a structural model using a locally risk-minimizing approach

In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Follmer–Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation Levy process and the claims pay a predetermined payout at maturity, contingent on no prior default. More precisely, in this particular framework, the locally risk-minimizing approach is carried out when the underlying process has jumps, the derivative is linked to a default event, and the probability measure is not necessarily risk-neutral.

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.

Good deal indices in asset pricing: actuarial and financial implications

We integrate into a single optimization problem a risk measure, beyond the variance, and either arbitrage free real market quotations or …financial pricing rules generated by an arbitrage free stochastic pricing model. A sequence of investment strategies such that the couple (expected-return, risk ) diverges to (+∞, -∞) will be called a good deal. The existence of such a sequence is equivalent to the existence of an alternative sequence of strategies such that the couple (risk, price) diverges to (-∞, -∞). Moreover, by appropriately adding the riskless asset, every good deal may generate a new one only composed of strategies priced at one. We will see that good deals often exist in practice, and the main objective of this paper will be to measure the good deal size. The provided good deal indices will equal an optimal ratio between both risk and price, and there will exist alternative interpretations of these indices. They also provide the minimum relative (per dollar) price modification that prevents the existence of good deals. Moreover, they will be a crucial instrument to detect those securities or marketed claims which are over- or under-priced. Many classical actuarial and …financial optimization problems may generate wrong solutions if the used market quotations or stochastic pricing models do not prevent the existence of good deals. This fact is illustrated in the paper, and we point out how the provided good deal indices may be useful to overcome this caveat. Numerical experiments are included as well.