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**Competitive optimal on-line leasing.**
*(English)*
Zbl 0955.91024

This paper regards the leasing or leasing-or-buy problem. In computer science this is known as the ski-rental problem. Using the competitive ratio as a performance measure this paper is concerned with determining the optimal competitive on-line policy. It regards both the deterministic and randomized optimal on-line leasing strategies while accounting for the interest rate factor.

It is shown, that the interest rate factor reduces the uncertainty involved. The optimal competitive ratio is a decreasing function of the interest. For some applications, realistic values of interest rates result in relatively low competitive rates. By using randomization the on-line player can boost up the performance.

The leasing problem against a distributional adversary called “Nature” is also studied. It is shown that the optimal competitive ratio against the Nature equals the optimal ratio against the oblivious adversary.

It is shown, that the interest rate factor reduces the uncertainty involved. The optimal competitive ratio is a decreasing function of the interest. For some applications, realistic values of interest rates result in relatively low competitive rates. By using randomization the on-line player can boost up the performance.

The leasing problem against a distributional adversary called “Nature” is also studied. It is shown that the optimal competitive ratio against the Nature equals the optimal ratio against the oblivious adversary.

Reviewer: Klaus Ehemann (Karlsruhe)

### MSC:

91B28 | Finance etc. (MSC2000) |

91A05 | 2-person games |