In this paper, the large deviation approach for computing the capital charge for operational risk of a bank is explored. Firstly, the negatively-associated structure is utilized to measure the dependence between distinct operational loss cells. Secondly, the lower and upper bounds of the tail distribution function of total aggregated loss processes are determined. In addition, first order appro...

Denote by X the set of actuarial risks, and let 0 ≤ X ∈ X be a random variable rv with cumulative distribution function cdf F x , decumulative distribution function ddf F x 1 − F x , and probability density function pdf f x . The functional H : X → 0,∞ is then referred to as a risk measure, and it is interpreted as the measure of risk inherent in X. Naturally, a quite significant number of risk...

In a general equilibrium model with risk neutral and risk averse agents, we show that if banks issue both demand deposits and equity, then free banking is run-proof and ecient. In particular, we obtain the ®rst best insurance solution if there is adequate risk neutral capital. If sucient risk neutral capital is unavailable, then a partial suspension of convertibility is optimal. In general, t...

Risk adjusted performance measurement for a portfolio involves calculating the contributions to total economic capital for sub-portfolios or single assets. We show that there is only one definition for the contributions which is suitable for performance measurement, namely as derivative of the underlying risk measure with respect to the weight of the considered sub-portfolio or asset. We review...

Maximum Relative Drawdown measures the largest percentage drop of the price process on a given time interval. Recently, Maximum Relative Drawdown has become more popular as an alternative measure of risk. In contrast to the Value at Risk measure, it captures the path property of the price process. In this article, we propose a partial differential equation approach to determine the theoretical ...

This paper analyzes individual bidding data from a series of sealed-bid auctions in which bidders do not known how many bidders they are bidding against. Unlike previous studies of sealed bid second price auctions with known number of bidders, we find a surprising amount of coincidence with theory. We observe systematic deviations from risk neutral bidding in first price auctions and show that ...

Let X be the solution of a stochastic differential equation driven by a Wiener process and a compensated Poisson random measure, such that X is an L martingale. If H = Φ(Xs; 0 ≤ s ≤ T ) is in L, then H = α+ ∫ T 0 ξsdXs +NT , where N is an L martingale orthogonal to X (the Kunita-Watanabe decomposition). We give sufficient conditions on the functional Φ such that ξ has regular paths (that is, le...

We propose an extension of the CPPI method, which is based on conditional floors. In this framework, we examine in particular the margin based strategies. This method allows to keep part of the past gains and to protect the portfolio value against future high drawdowns of the financial market. However, as for the standard CPPI method, the investor can benefit from potential market rises. To con...

In quantitative risk management, it is important and challenging to find sharp bounds for the distribution of the sum of dependent risks with given marginal distributions, but an unspecified dependence structure. These bounds are directly related to the problem of obtaining the worst Value-at-Risk of the total risk. Using the idea of the complete mixability, we provide a new lower bound for any...