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Seminários do IMPA

Métodos Matemáticos em Finanças

Título |
Incomplete markets |

Expositor |
Teemu Pennanen
King's College London |

Data |
Quinta-feira, 5 de abril de 2018, 17:30 |

Local |
Sala 232 |

Resumo |

This is the second of a set of 4 lectures so as to give an introduction to asset-liability management, accounting and indifference pricing in terms of basic optimization theory. Our aim is to give a unified treatment of the above concepts and to study their relations and basic properties with minimal mathematical sophistication. Mathematical techniques are introduced only when they become necessary for the development of the theory. Working with discrete-time models allows us to avoid many of the technicalities associated with continuous time models. This leaves room for practical considerations that are sometimes neglected in more mathematiWorking with discrete-time models allows us to avoid many of the technicalities associated with continuous time models. This leaves room for practical considerations that are sometimes neglected in more mathematical texts. In particular, we extend the classical theory of mathematical finance by allowing for nonlinear illiquidity effects and portfolio constraints.

Such features are significant in practice but they invalidate much of the classical theory. We deviate from the classical theory also in that we do not insist on the existence of a perfectly liquid numeraire asset. This means that one can no longer postpone payments by shorting the numeraire so the payment schedule of a financial contract becomes an important issue. This is essential in practice where much of trading consists of exchanging sequences of cash-flows. Examples include loans as well as various swap and insurance contracts where both claims and premiums involve payments at several points in time.cal texts. In particular, we extend the classical theory of mathematical finance by allowing for nonlinear illiquidity effects and portfolio constraints.

Such features are significant in practice but they invalidate much of the classical theory. We deviate from the classical theory also in that we do not insist on the existence of a perfectly liquid numeraire asset. This means that one can no longer postpone payments by shorting the numeraire so the payment schedule of a financial contract becomes an important issue. This is essential in practice where much of trading consists of exchanging sequences of cash-flows. Examples include loans as well as various swap and insurance contracts where both claims and premiums involve payments at several points in time.