For a continuous-time financial market with a single agent, we establish equilibrium pricing formulae under the assumption that the dividends follow an exponential Lévy process. The agent is allowed to consume a lump at the terminal date; before, only flow consumption is allowed. The agent's...

For a continuous-time financial market with a single agent, we establish equilibrium pricing formulae under the assumption that the dividends follow an exponential Lévy process. The agent is allowed to consume a lump at the terminal date; before, only flow consumption is allowed. The agent's...

For a continuous-time financial market with a single agent, we establish equilibrium pricing formulae under the assumption that the dividends follow an exponential Lévy process. The agent is allowed to consume a lump at the terminal date; before that, only flow consumption is allowed. The...

This article shows that the nonstandard approach to stochastic integration with respect to (C² functions of) Lévy processes is consistent with the classical theory of pathwise stochastic integration with respect to (C² functions of) jump-diffusions with finite-variation jump part. It is...

This article shows that the nonstandard approach to stochastic integration with respect to (C^2 functions of) Lévy processes is consistent with the classical theory of pathwise stochastic integration with respect to (C^2 functions of) jump-diffusions with finite-variation jump part.It is proven...

This article links the hyperfinite theory of stochastic integration with respect to certain hyperfinite Lévy processes with the elementary theory of pathwise stochastic integration with respect to pure-jump Lévy processes with finite-variation jump part. Since the hyperfinite Itô integral is...

The paradox of the Stop-Loss-Start-Gain trading strategy is resolved by showing that along the hyperfinite timeline the strategy incurs infinitesimal losses summing up to a non-infinitesimal amount. As a consequence, the Black–Scholes formula is derived using only hyperreal arithmetic and...

In a two-period pure exchange economy with financial assets, a temporary financial equilibrium is an equilibrium of the current spot and security markets given forecast functions of future prices and payoffs. The temporary equilibrium model can then be interpreted as an Arrow-Debreu economy...

This paper explores the role of portfolio constraints in generating multiplicity of equilibrium. We present a simple financial market economy with two goods and two households, households who face constraints on their ability to take unbounded positions in risky stocks. Absent such constraints,...