caa a22 4500 467922365 CHVBK 20180406152920.0 cr unu---uuuuu 170328e20060401xx s 000 0 eng 10.1007/s00477-005-0001-x doi (NATIONALLICENCE)springer-10.1007/s00477-005-0001-x Equilibrium trading of climate and weather risk and numerical simulation in a Markovian framework [Elektronische Daten] [Sébastien Chaumont, Peter Imkeller, Matthias Müller] 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 marketalone, 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. Springer-Verlag, 2005 primary 60 H 30, 91 B 70 nationallicence secondary 60 H 20, 91 B 28, 91 B 76, 91 B 30, 93 E 20, 35 K 55 nationallicence External risk nationallicence Climate risk nationallicence ENSO nationallicence Incomplete financial market nationallicence Utility maximization nationallicence Exponential utility nationallicence Market equilibrium nationallicence Market clearing nationallicence Backward stochastic differential equation nationallicence Semi-linear parabolic pde nationallicence Non-linear Feynman-Kac formula nationallicence HJB equation nationallicence Numerical schemes for pde nationallicence Numerical simulation nationallicence Chaumont Sébastien Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut Imkeller Peter Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut Müller Matthias Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut Stochastic Environmental Research and Risk Assessment Springer-Verlag 20/3(2006-04-01), 184-205 1436-3240 20:3<184 2006 20 477 https://doi.org/10.1007/s00477-005-0001-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00477-005-0001-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chaumont Sébastien Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut NATIONALLICENCE 700 1- Imkeller Peter Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut NATIONALLICENCE 700 1- Müller Matthias Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut NATIONALLICENCE 773 0- Stochastic Environmental Research and Risk Assessment Springer-Verlag 20/3(2006-04-01), 184-205 1436-3240 20:3<184 2006 20 477 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer