Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

PATH DECOMPOSITION OF RUINOUS BEHAVIOR FOR A GENERAL LÉVY INSURANCE RISK PROCESS

Philip S. Griffin and Ross A. Maller
The Annals of Applied Probability
Vol. 22, No. 4 (August 2012), pp. 1411-1449
Stable URL: http://www.jstor.org/stable/41713364
Page Count: 39
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
PATH DECOMPOSITION OF RUINOUS BEHAVIOR FOR A GENERAL LÉVY INSURANCE RISK PROCESS
Preview not available

Abstract

We analyze the general Lévy insurance risk process for Lévy measures in the convolution equivalence class S⁽ α ⁾, α > 0, via a new kind of path decomposition. This yields a very general functional limit theorem as the initial reserve level u → ∞, and a host of new results for functional of interest in insurance risk. Particular emphasis is placed on the time to ruin, which is shown to have a proper limiting distribution, as u → ∞, conditional on ruin occurring under our assumptions. Existing asymptotic results under the S⁽ α ⁾ assumption are synthesized and extended, and proofs are much simplified, by comparison with previous methods specific to the convolution equivalence analyses. Additionally, limiting expressions for penalty functions of the type introduced into actuarial mathematics by Gerber and Shiu are derived as straightforward applications of our main results.

Page Thumbnails

  • Thumbnail: Page 
1411
    1411
  • Thumbnail: Page 
1412
    1412
  • Thumbnail: Page 
1413
    1413
  • Thumbnail: Page 
1414
    1414
  • Thumbnail: Page 
1415
    1415
  • Thumbnail: Page 
1416
    1416
  • Thumbnail: Page 
1417
    1417
  • Thumbnail: Page 
1418
    1418
  • Thumbnail: Page 
1419
    1419
  • Thumbnail: Page 
1420
    1420
  • Thumbnail: Page 
1421
    1421
  • Thumbnail: Page 
1422
    1422
  • Thumbnail: Page 
1423
    1423
  • Thumbnail: Page 
1424
    1424
  • Thumbnail: Page 
1425
    1425
  • Thumbnail: Page 
1426
    1426
  • Thumbnail: Page 
1427
    1427
  • Thumbnail: Page 
1428
    1428
  • Thumbnail: Page 
1429
    1429
  • Thumbnail: Page 
1430
    1430
  • Thumbnail: Page 
1431
    1431
  • Thumbnail: Page 
1432
    1432
  • Thumbnail: Page 
1433
    1433
  • Thumbnail: Page 
1434
    1434
  • Thumbnail: Page 
1435
    1435
  • Thumbnail: Page 
1436
    1436
  • Thumbnail: Page 
1437
    1437
  • Thumbnail: Page 
1438
    1438
  • Thumbnail: Page 
1439
    1439
  • Thumbnail: Page 
1440
    1440
  • Thumbnail: Page 
1441
    1441
  • Thumbnail: Page 
1442
    1442
  • Thumbnail: Page 
1443
    1443
  • Thumbnail: Page 
1444
    1444
  • Thumbnail: Page 
1445
    1445
  • Thumbnail: Page 
1446
    1446
  • Thumbnail: Page 
1447
    1447
  • Thumbnail: Page 
1448
    1448
  • Thumbnail: Page 
1449
    1449