1,051 research outputs found
Predictable projections of conformal stochastic integrals: an application to Hermite series and to Widder's representation
In this article, we study predictable projections of stochastic integrals
with respect to the conformal Brownian motion, extending the connection between
powers of the conformal Brownian motion and the corresponding Hermite
polynomials. As a consequence of this result, we then investigate the relation
between analytic functions and -convergent series of Hermite polynomials.
Finally, our results are applied to Widder's representation for a class of
Brownian martingales, retrieving a characterization for the moments of Widder's
measure.Comment: 16 pages. Added keywords, MSC classification, contact informatio
Hedging under arbitrage
It is shown that delta hedging provides the optimal trading strategy in terms
of minimal required initial capital to replicate a given terminal payoff in a
continuous-time Markovian context. This holds true in market models where no
equivalent local martingale measure exists but only a square-integrable market
price of risk. A new probability measure is constructed, which takes the place
of an equivalent local martingale measure. In order to ensure the existence of
the delta hedge, sufficient conditions are derived for the necessary
differentiability of expectations indexed over the initial market
configuration. The recently often discussed phenomenon of "bubbles" is a
special case of the setting in this paper. Several examples at the end
illustrate the techniques described in this work.Comment: Minor changes, accepted for publication in Journal of Mathematical
Financ
Surplus sharing with coherent utility functions
We use the theory of coherent measures to look at the problem of surplus
sharing in an insurance business. The surplus share of an insured is calculated
by the surplus premium in the contract. The theory of coherent risk measures
and the resulting capital allocation gives a way to divide the surplus between
the insured and the capital providers, i.e. the shareholders
Stability of the utility maximization problem with random endowment in incomplete markets
We perform a stability analysis for the utility maximization problem in a
general semimartingale model where both liquid and illiquid assets (random
endowments) are present. Small misspecifications of preferences (as modeled via
expected utility), as well as views of the world or the market model (as
modeled via subjective probabilities) are considered. Simple sufficient
conditions are given for the problem to be well-posed, in the sense the optimal
wealth and the marginal utility-based prices are continuous functionals of
preferences and probabilistic views.Comment: 21 pages, revised version. To appear in "Mathematical Finance"
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