Asymptotic Distributions of the Overshoot and Undershoots for the L\'evy Insurance Risk Process in the Cram\'er and Convolution Equivalent Cases

Recent models of the insurance risk process use a L\'evy process to generalise the traditional Cram\'er-Lundberg compound Poisson model. This paper is concerned with the behaviour of the distributions of the overshoot and undershoots of a high level, for a L\'{e}vy process which drifts to $-\infty$ and satisfies a Cram\'er or a convolution equivalent condition. We derive these asymptotics under minimal conditions in the Cram\'er case, and compare them with known results for the convolution equivalent case, drawing attention to the striking and unexpected fact that they become identical when certain parameters tend to equality. Thus, at least regarding these quantities, the "medium-heavy" tailed convolution equivalent model segues into the "light-tailed" Cram\'er model in a natural way. This suggests a usefully expanded flexibility for modelling the insurance risk process. We illustrate this relationship by comparing the asymptotic distributions obtained for the overshoot and undershoots, assuming the L\'evy process belongs to the "GTSC" class

Diversification Meltdown or the Impact of Fat tails on Conditional Correlation?

A perceived increase in correlation during turbulent market conditions implies a reduction in the benefits arising from portfolio diversification. Unfortunately, it is exactly then that these benefits are most needed. To determine whether diversification truly breaks down, we investigate the robustness of a popular conditional correlation estimator against alternative distributional assumptions. Analytical results show that the apparent meltdown in the benefits from diversification could be a consequence of assuming normally distributed returns. A more realistic assumption - the bivariate Student-t distribution - suggests that constant correlation may be sustained over the full support of the multivariate return distributionConditional correlation, Truncated correlation, Bivariate Student-t correlation.

Pricing Higher-Dimensional American Options Using The Stochastic Grid Method

This paper considers the problem of pricing options with early-exercise features whose payo depends on several sources of uncertainty. We propose a stochastic grid method for estimating the upper and lower bound values of high-dimensional American options. The method is a hybrid of the least squares method of Longsta and Schwartz (2001) [22], the stochastic mesh method of Broadie and Glasserman (2004) [11], and stratified state aggregation along the pay-off method of Barraquand and Martineau (1995) [3]. Numerical results are given for single asset Bermudan options, Bermudan max options, Bermudan options on the arithmetic mean of a collection of stocks

Pearson Codes

The Pearson distance has been advocated for improving the error performance of noisy channels with unknown gain and offset. The Pearson distance can only fruitfully be used for sets of $q$-ary codewords, called Pearson codes, that satisfy specific properties. We will analyze constructions and properties of optimal Pearson codes. We will compare the redundancy of optimal Pearson codes with the redundancy of prior art $T$-constrained codes, which consist of $q$-ary sequences in which $T$ pre-determined reference symbols appear at least once. In particular, it will be shown that for $q\le 3$ the $2$-constrained codes are optimal Pearson codes, while for $q\ge 4$ these codes are not optimal.Comment: 17 pages. Minor revisions and corrections since previous version. Author biographies added. To appear in IEEE Trans. Inform. Theor

Decision-support tool for assessing future nuclear reactor generation portfolios

Capital costs, fuel, operation and maintenance (O&M) costs, and electricity prices play a key role in the economics of nuclear power plants. Often standardized reactor designs are required to be locally adapted, which often impacts the project plans and the supply chain. It then becomes difficult to ascertain how these changes will eventually reflect in costs,which makes the capital costs component of nuclear power plants uncertain. Different nuclear reactor types compete economically by having either lower and less uncertain construction costs, increased efficiencies, lower and less uncertain fuel cycles and O&M costs etc. The decision making process related to nuclear power plants requires a holistic approach that takes into account the key economic factors and their uncertainties. We here present a decision-support tool that satisfactorily takes into account the major uncertainties in the cost elements of a nuclear power plant, to provide an optimal portfolio of nuclear reactors. The portfolio so obtained, under our model assumptions and the constraints considered, maximizes the combined returns for a given level of risk or uncertainty. These decisions are made using a combination of real option theory and mean–variance portfolio optimization

Valuing modular nuclear power plants in finite time decision horizon

Small and medium sized reactors, SMRs, (according to IAEA, ‘small’ refers to reactors with power less than 300 MWe, and ‘medium’ with power less than 700 MWe) are considered as an attractive option for investment in nuclear power plants. SMRs may benefit from flexibility of investment, reduced upfront expenditure, enhanced safety, and easy integrationwith small sized grids. Large reactors on the other hand have been an attractive option due to the economy of scale. In this paper we focus on the economic impact of flexibility due to modular construction of SMRs. We demonstrate, using real option analysis, the value of sequential modular SMRs. Numerical results under different considerations of decision time, uncertainty in electricity prices, and constraints on the construction of units, are reported for a single large unit and for modular SMRs