The trap of complacency in predicting the maximum.
By Jacques Du Toit, Goran Peskir. 2007
73 citations recorded by the source corpus.
„where t⁄ 2 [0;T) and the functions t 7! b1(t) and t 7! b2(t) are continuous on [t⁄;T] with b1(T)=0 and b2(T)=1=2„ . If „ > 0 then b1 is decreasing and b2 is increasing on [t⁄;T] with b1(t⁄) = b2(t⁄) when t⁄ 6 0 . Using local time-space calculus we derive a coupled system of nonlinear Volterra integral equations of the second kind and show that the pair of optimal boundaries b1 and b2 can be characterized as the unique solution to this system. This also leads to an explicit formula for V in terms of b1 and b2 . If „ • 0 then t⁄ = 0 and b2 · +1 so that ?⁄ is expressed in terms of b1 only. In this case b1 is decreasing on [z⁄;T] and increasing on [0;z⁄) for some z⁄ 2 [0;T) with z⁄ = 0 if „ = 0 , and the system of two Volterra equations reduces to one Volterra equation. If „ = 0 then there is a closed form expression for b1 . This problem was solved in [6] using the method of time change (i.e. change of variables). The method of time change cannot be extended to the case when „ 6 0 and the present paper settles the remaining cases using a difierent approach.
Subfields: Finance, Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/a01d1fe2d1aa61c1ccd53bdfe095edbeb001c3d8
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Citations in the corpus
- Selling a Stock at the Ultimate Maximum (2009, background): “0,T] at any point x in the state space. It is therefore especially important to see how X depends on its starting value x. Although the equation for Y is difficult to solve explicitly, it is known (cf. [2], Lemma 2.2 and [11], Theorem 2.1) that the Markov process Xx =(Xx t ) 0≤t≤T defined under Pas X x”