TY - THES
AU - Moreno-Bromberg, Santiago
PY - 2008
TI - Optimal design of over-the-counter derivatives in a principal-agent framework : an existence result and numerical implementations
KW - Thesis/Dissertation
LA - eng
M3 - Text
AB - This work lies in the intersection of Mathematical Finance, Mathematical
Economics and Convex Analysis. In terms of the latter, a new result (to the
author’s knowledge) on a Lipschitz property of the derivatives of a convex
function is presented in the first chapter. An important result on its own,
it might also provide a stepping stone to an extension to Hubert spaces of
Alexandrov’s theorem on the second derivatives of convex functions.
The second chapter considers the problem of Adverse Selection and op
timal derivative design within a Principal-Agent framework. The principal’s
income is exposed to non-hedgeable risk factors arising, for instance, from
weather or climate phenomena. She evaluates her risk using a coherent and
law invariant risk measure and tries to minimize her exposure by selling
derivative securities on her income to individual agents. The agents have
mean-variance preferences with heterogeneous risk aversion coefficients. An
agent’s degree of risk aversion is private information and the principal only
knows their overall distribution. It is shown that the principal’s risk mini
mization problem has a solution and, in terms of the pricing schedule, the
latter is unique.
Finding a solution to the principal’s problem requires solving a varia
tional problem with global convexity constraints. In general, this cannot be
done in closed form. To this end an algorithm to approximate the solutions
to variational problems where set of admissible functions consists of convex
functions is presented in the fourth chapter of this work. Several examples
are provided.
N2 - This work lies in the intersection of Mathematical Finance, Mathematical
Economics and Convex Analysis. In terms of the latter, a new result (to the
author’s knowledge) on a Lipschitz property of the derivatives of a convex
function is presented in the first chapter. An important result on its own,
it might also provide a stepping stone to an extension to Hubert spaces of
Alexandrov’s theorem on the second derivatives of convex functions.
The second chapter considers the problem of Adverse Selection and op
timal derivative design within a Principal-Agent framework. The principal’s
income is exposed to non-hedgeable risk factors arising, for instance, from
weather or climate phenomena. She evaluates her risk using a coherent and
law invariant risk measure and tries to minimize her exposure by selling
derivative securities on her income to individual agents. The agents have
mean-variance preferences with heterogeneous risk aversion coefficients. An
agent’s degree of risk aversion is private information and the principal only
knows their overall distribution. It is shown that the principal’s risk mini
mization problem has a solution and, in terms of the pricing schedule, the
latter is unique.
Finding a solution to the principal’s problem requires solving a varia
tional problem with global convexity constraints. In general, this cannot be
done in closed form. To this end an algorithm to approximate the solutions
to variational problems where set of admissible functions consists of convex
functions is presented in the fourth chapter of this work. Several examples
are provided.
UR - https://open.library.ubc.ca/collections/24/items/1.0066987
ER - End of Reference