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BEGIN:VEVENT
DTSTAMP:20260209T140205Z
DTSTART:20260211T150000Z
DTEND:20260211T160000Z
SUMMARY:Probability Seminar: Jose Pedraza Ramirez - Optimal Prediction of
  the Last r-Excursion Time of Brownian Motion Models
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}n1m6-mlf8qx
 84-2q49hb
DESCRIPTION:Jose Pedraza Ramirez (University of Manchester) will speak at
  the Probability seminar.\n\n\nTitle: Optimal Prediction of the Last r-E
 xcursion Time of Brownian Motion Models\n\nAbstract:\n\nWe investigate t
 he optimal prediction of the last $r$-excursion time for a Brownian moti
 on model. The last $r$-excursion time\, denoted by $l_{r}$\, refers to t
 he right endpoint of the last negative excursion lasting longer than a c
 onstant $r>0$. It reduces to the standard last passage time when $r\\dow
 narrow 0$. For a Brownian motion with drift $\\mu >0$ and volatility $\\
 sigma >0$\, our goal is to identify an optimal stopping time that minimi
 ses the ($L_{1}$) distance from the last $r$-excursion time $l_{r}$. We 
 find that the optimal stopping barrier exhibits two distinct structures:
  a constant barrier (characterized as a solution of a non-linear equatio
 n) or a moving barrier (characterised by the unique solution to an integ
 ral equation) depending on the ratio $R=\\frac{\\mu \\sqrt{r}}{\\sigma }
 $ which integrates a firm's financial profitability\, volatility\, and r
 isk tolerance to financial distress. To obtain the optimal stopping time
 \, we examine the smooth fit condition\, Lipschitz continuity of the bar
 rier\, and probability regularity of the boundary points. As an applicat
 ion in risk management\, we develop a decision rule that informs the tim
 ing of business expansion and contraction.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 2\, Alan Turing Building\, Manchester
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