Average Performance of Passive Algorithms for Global Optimization

Calvin, James M.

doi:10.1006/jmaa.1995.1151

Cited by 23 publications

(29 citation statements)

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“…This result is used to establish that the order of strong convergence when a reflected Brownian motion is simulated using the Euler discretization is 1 2 . The same result is also derived in [6], although in a different form, when two passive algorithms for global optimization of continuous functions on onedimensional domains are studied. The coefficient for 1/N is further derived in [5] when correction formulae are designed for pricing discretely monitored lookback options using continuous lookback option pricing formulae in the Black-Scholes-Merton model.…”

Section: Introduction and Main Resultssupporting

confidence: 50%

On the Monitoring Error of the Supremum of a Normal Jump Diffusion Process

Chen

Feng

Song³

2011

J. Appl. Probab.

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We derive an expansion for the (expected) difference between the continuously monitored supremum and evenly monitored discrete maximum over a finite time horizon of a jump diffusion process with independent and identically distributed normal jump sizes. The monitoring error is of the form a 0 /N 1/2 +a 1 /N 3/2 +· · ·+b 1 /N +b 2 /N 2 +b 4 /N 4 +· · · , where N is the number of monitoring intervals. We obtain explicit expressions for the coefficients {a 0 , a 1 , . . . , b 1 , b 2 , . . .}. In particular, a 0 is proportional to the value of the Riemann zeta function at 1 2 , a well-known fact that has been observed for Brownian motion in applied probability and mathematical finance.

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Section: Introduction and Main Resultssupporting

confidence: 50%

On the Monitoring Error of the Supremum of a Normal Jump Diffusion Process

Chen

Feng

Song³

2011

J. Appl. Probab.

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“…Adapting this procedure to the trinomial method gives improved convergence as shown in the middle panel on Table 5. 15 Two-point extrapolation using equation (15) further improves matters. Alternatively, we can adapt the first-order approximation in equation (17) to adjust the output of the discrete trinomial method for approximating the continuous lookback price.…”

Section: Lattice Methods For Continuous Lookback Optionsmentioning

confidence: 99%

“…For example, using n = 25 steps, the price in Table 5 with the standard method is 9.36106, but the corrected value using equation (18) is 10.83824. Complete results using equation (18) and two-point extrapolation using equation (15) are given in the right panel of Table 5. The convergence of Babbs' "reflected trinomial" method and of the "corrected trinomial" method (with and without extrapolation) are essentially indistinguishable and both are clearly superior to the standard method.…”

Section: Lattice Methods For Continuous Lookback Optionsmentioning

confidence: 99%

“…The left panel holds λ constant at 1.02, the middle panel holds λ constant at 1.42, and in the right panel λ alternates between the two values. When λ is constant at either 1.02 or 1.42, convergence of the trinomial price is monotonic, and extremely rapid convergence is obtained using the two-point extrapolation formula (15). However, when λ alternates the trinomial values are not monotonic, and extrapolation actually slows convergence.…”

Section: Lattice Methods For Continuous Lookback Optionsmentioning

confidence: 99%

“…For the price of a lookback at inception we derive a second-order approximation based on the second moment of one of these limiting distributions. The role of β 1 in discrete barrier options is rooted in work of Chernoff [17] 2 and Siegmund and Yuh [58] on diffusion approximations to random walks; its role in discrete lookback options is rooted in the analysis of Calvin [15] and Asmussen, Glynn, and Pitman [5] on the maximum of Brownian motion.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Connecting discrete and continuous path-dependent options

Broadie

Glasserman

Kou³

1999

Finance and Stochastics

178

143

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Abstract. This paper develops methods for relating the prices of discrete-and continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpreted as shifting a barrier, a strike, or an extremal price. These correction terms enable us to use closed-form solutions for continuous option prices to approximate their discrete counterparts. We also develop discrete-time discrete-state lattice methods for determining accurate prices of discrete and continuous path-dependent options. In several cases, the lattice methods use correction terms based on the connection between discrete-and continuous-time prices which dramatically improve convergence to the accurate price.

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Average performance of adaptive algorithms for programming co-ordinate measuring machines under budget constraint

Al-Mharmah

1999

Appl. Stochastic Models Data Anal.

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Average Performance of Passive Algorithms for Global Optimization

Cited by 23 publications

References 0 publications

On the Monitoring Error of the Supremum of a Normal Jump Diffusion Process

On the Monitoring Error of the Supremum of a Normal Jump Diffusion Process

Connecting discrete and continuous path-dependent options

Average performance of adaptive algorithms for programming co-ordinate measuring machines under budget constraint

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