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Short term climate events such as the sea surface temperature anomaly known as El Nino are financial risk sources leading to incomplete markets. To make such risk tradable, we use a market model in which a climate index provides an extra investment opinion. Given one possible market price of risk each agent can maximize the exponential utility from three sources of income: capital market, additional security, and individual risk exposure. Under an equilibrium condition the market price of risk is uniquely determined by a backward stochastic differential equation. We translate these stochastic equations into semi-linear partial differential equations for the simulation of which numerical schemes are available. We choose two simple models for sea surface temperature, and with ENSO risk exposed fisher and farmer and a nonh-exposed bank three toy agents. By simulating their optimal investment into the climat index we obtain first insight into the dynamics of the market.
The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one dimensional parametrized stochastic differential equation with point delay, basic properties whereof we check. With a view to capturing the effective dynamics and, in particular, the resonance-like behaviour of the reference model we construct a simplified or reduced model, the two state model, first in discrete time, then in the limit of discrete time tending to continuous time. The main advantage of the reduced model is that it enables us to explicitly calculate the distribution of residence times which in turn can be used to characterize the phenomenon of noise-induced resonance. Drawing on what has been proposed in the physics literature, we outline a heuristic method for establishing the link between the two state model and the reference model. The resonance characteristic developed for the reduced model can thus be applied to the original model.
The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one dimensional parametrized stochastic differential equation with point delay, basic properties whereof we check.
With a view to capturing the effective dynamics and, in particular, the resonance-like behaviour of the reference model we construct a simplified or reduced model, the two state model, first in discrete time, then in the limit of discrete time tending to continuous time. The main advantage of the reduced model is that it enables us to explicitly calculate the distribution of residence times which in turn
can be used to characterize the phenomenon of noise-induced resonance.
Drawing on what has been proposed in the physics literature, we outline a heuristic method for establishing the link between the two state model and the reference model. The resonance characteristic developed for the reduced model can thus be applied to the original model.