Knut K. Aase

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This paper attempts to give an overview of the pricing of risks in a pure exchange economy, where trade takes place at time zero and where uncertainty is revealed at time one. An economic equilibrium model under uncertainty is formulated, where conditions characterizing a Pareto optimal exchange equilibrium are derived. We present two sets of sufficient(More)
We use a white noise approach to Malliavin calculus to prove the following white noise generalization of the Clark-Haussmann-Ocone formula F (ω) = E[F ] + T 0 E[D t F |F t ] W (t)dt Here E[F ] denotes the generalized expectation, D t F (ω) = dF dω is the (generalized) Malliavin derivative, is the Wick product and W (t) is 1-dimensional Gaussian white noise.(More)
The continuous-time version of Kyle’s (1985) model of asset pricing with asymmetric information is studied, and generalized in various directions, i.e., by allowing time-varying liquidity trading, and by having weaker a priori assumptions on the model. This extension is made possible by the use of filtering theory. We derive the optimal trade for an insider(More)
We use a white noise approach to Malliavin calculus to prove the following white noise generalization of the Clark-Haussmann-Ocone formula F (ω) = E[F ] + T 0 E[D t F |F t ] ⋄ W (t)dt Here E[F ] denotes the generalized expectation, D t F (ω) = dF dω is the (generalized) Malliavin derivative,⋄ is the Wick product and W (t) is 1-dimensional Gaussian white(More)
We reconsider costs in insurance, and suggest a new type of cost function, which we argue is a natural choice when there are relatively small, but frequent, claims. If a fixed cost is incurred each time a claim is made, we obtain a Pareto optimal deductible even if the cost function does not vary with the indemnity. The classical result says that(More)
In an editorial in ASTIN BULLETIN, Hans Bühlmann (2002) suggests it is time to change the teaching of life insurance theory towards the real life challenges of that industry. The following note is a response to this editorial. In Bergen we have partially taught the NUMAT, or the NUMeraire based Actuarial Teaching since the beginning of the 90ties at the(More)
In the classical Kalman-Bucy filter and in the subsequent literature so far, it has been assumed that the initial value of the signal process is independent of both the noise of the signal and of the noise of the observations. The purpose of this paper is to prove a filtering equation for a linear system where the (normally distributed) initial value X0 of(More)
A standard result states that under decreasing absolute risk aversion the indifference premium of the insured is a decreasing function of wealth. This has been interpreted to mean that insurance is an inferior good, which has been considered as a puzzle in insurance theory, in particular since the result does not seem to explain observed behavior in(More)