Equilibrium trading of climate and weather risk and numerical simulation in a Markovian framework |
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| Authors: | Sébastien Chaumont Peter Imkeller Matthias Müller |
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| Institution: | 1. Institut für Mathematik, Humboldt-Universit?t zu Berlin, Unter den Linden 6, 10099, Berlin, Germany
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| Abstract: | We consider financial markets with agents exposed to external sources of risk caused, for example, by short-term climate events
such as the South Pacific sea surface temperature anomalies widely known by the name El Nino. Since such risks cannot be hedged
through investments on the capital market alone, we face a typical example of an incomplete financial market. In order to
make this risk tradable, we use a financial market model in which an additional insurance asset provides another possibility
of investment besides the usual capital market. Given one of the many possible market prices of risk, each agent can maximize
his individual exponential utility from his income obtained from trading in the capital market, the additional security, and
his risk-exposure function. Under the equilibrium market-clearing condition for the insurance security the market price of
risk is uniquely determined by a backward stochastic differential equation. We translate these stochastic equations via the
Feynman–Kac formalism into semi-linear parabolic partial differential equations. Numerical schemes are available by which
these semilinear pde can be simulated. We choose two simple qualitatively interesting models to describe sea surface temperature,
and with an ENSO risk exposed fisher and farmer and a climate risk neutral bank three model agents with simple risk exposure
functions. By simulating the expected appreciation price of risk trading, the optimal utility of the agents as a function
of temperature, and their optimal investment into the risk trading security we obtain first insight into the dynamics of such
a market in simple situations.
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| Keywords: | 2000 AMS subject classifications:" target="_blank">2000 AMS subject classifications: primary 60 H 30 91 B 70 secondary 60 H 20 91 B 28 91 B 76 91 B 30 93 E 20 35 K 55 |
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