# A note on the forward measure

## Author

Listed:
• Mark Davis

(Tokyo-Mitsubishi International plc, 6 Broadgate, London EC2M 2AA, UK)

## Abstract

For a Markov process $x_t$, the forward measure $P^T$ over the time interval $[0,T]$ is defined by the Radon-Nikodym derivative $dP^T/dP = M\exp(-\int_0^Tc(x_s)ds)$, where $c$ is a given non-negative function and $M$ is the normalizing constant. In this paper, the law of $x_t$ under the forward measure is identified when $x_t$ is a diffusion process or, more generally, a continuous-path Markov process.

## Suggested Citation

• Mark Davis, 1997. "A note on the forward measure," Finance and Stochastics, Springer, vol. 2(1), pages 19-28.
• Handle: RePEc:spr:finsto:v:2:y:1997:i:1:p:19-28
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## References listed on IDEAS

as
1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
2. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276.
3. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
Full references (including those not matched with items on IDEAS)

### Keywords

Risk-neutral measure; Radon-Nikodym derivative; option pricing;

### JEL classification:

• G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
• C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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