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2 results

  • A Note on a Paper by Wong and Heyde

  • Part of
  • Aleksandar Mijatović, Mikhail Urusov
  • Journal:
    Journal of Applied Probability / Volume 48 / Issue 3 / September 2011
    Published online by Cambridge University Press:
    14 July 2016, pp. 811-819
    Print publication:
    September 2011
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  • In this note we re-examine the analysis of the paper ‘On the martingale property of stochastic exponentials’ by Wong and Heyde (2004). Some counterexamples are presented and alternative formulations are discussed.

  • What is the time value of a stream of investments?

  • Part of
  • Ragnar Norberg, Mogens Steffensen
  • Journal:
    Journal of Applied Probability / Volume 42 / Issue 3 / September 2005
    Published online by Cambridge University Press:
    14 July 2016, pp. 861-866
    Print publication:
    September 2005
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  • The titular question is investigated for fairly general semimartingale investment and asset price processes. A discrete-time consideration suggests a stochastic differential equation and an integral expression for the time value in the continuous-time framework. It is shown that the two are equivalent if the jump part of the price process converges. The integral expression, which is the answer to the titular question, is the sum of all investments accumulated with returns on the asset (a stochastic integral) plus a term that accounts for the possible covariation between the two processes. The arbitrage-free price of the time value is the expected value of the sum (i.e. integral) of all investments discounted with the locally risk-free asset.