We show how the well-known Farkas Lemma, commonly used to characterise absence of arbitrages in perfect markets, is also exploitable to ascertain the completeness of a market with total short sales constraints. The generalisation of this lemma to convex cones also allows to characterise the...

We show how the well-known Farkas Lemma, commonly used to characterise absence of arbitrages in perfect markets, is also exploitable to ascertain the completeness of a market with total short sales constraints. The generalisation of this lemma to convex cones also allows to characterise the...

The valuation theory for American Contingent Claims, due to Bensoussan (1984) and Karatzas (1988), is extended to deal with constraints on portfolio choice, including incomplete markets and borrowing/short-selling constraints, or with different interest rates for borrowing and lending. In the...

We present a new approach for continuous-time portfolio strategies that relies on the principle of value preservation. This principle was developed by Hellwig (1987) for general economic decision and pricing models. The key idea is that an investor should try to consume only so much of his...

We present a new approach for continuous-time portfolio strategies that relies on the principle of value preservation. This principle was developed by Hellwig (1987) for general economic decision and pricing models. The key idea is that an investor should try to consume only so much of his...