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In recent years, stress testing has become a regulatory requirement for risk assessment in financial institutions. To perform stress testing in multi-asset case, adjusting the correlation matrix to an extreme level is an important process. With a larger matrix, it is more difficult to choose the right correlation coefficients such that the newly adjusted correlation matrix is still valid. In this article, we present a systematic way to obtain the boundaries of a correlation matrix for both single stress and multiple stress cases, which can help determine how much the correlation should be adjusted in the first place.

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Mathematical models of host-pathogen interactions are proposed and analyzed. Here hosts are oyster population in a free-swimming larval stage and assumably live in the closed homogeneous environment. In terms of an epidemic, they are classified into two states, namely susceptible and infectious hosts. The epidemic model of oyster hosts with seasonal forced transmission is firstly described by the SIS model where the region of attraction, the existence of equilibrium points, their stability conditions, and upper and lower bounds on the attack rate are investigated. Then free-living pathogen is introduced in the oyster area. Numerical simulations are finally carried out by making use of the various salinity-dependent transmissions in support of the hypothesis that the lower the salinity level, the lower oyster’s immunity.

The aim of this paper is to investigate harvest-induced evolution in life-history strategies of a harvested single-species population. In particular, we analyze evolution of the trait age at first reproduction. The population is grouped into four age classes, namely, zero-year-olds (newborns), one-year-olds (juveniles), two-year-olds (small adults), and individuals aged three years or older (large adults). The population is assumed to consist of a 'resident' group and a 'variant' group that are identical except that the resident group usually first reproduces as a large adult and the variant group usually first reproduces as a small adult. The effect of various age-dependent harvesting strategies on the dynamics is studied both analytically and numerically. It is shown that age-dependent harvesting strategies can cause evolution from the resident group to the variant group. In addition, we show that a limit on the harvesting of the resident group can yield a sustainable fishery of the commercially preferred resident group. MSC: 39A30; 92B05