Advances in Risk Management

16 DETERMINATION OF THE CAPITAL CHARGE FOR OPERATIONAL RISK Table 1.5 Summary results for BL1 and BL2 (collection threshold=0.25 ...

YVES CRAMA, GEORGES HÜBNER AND JEAN-PHILIPPE PETERS 17 Table 1.6Estimated frequency and severity distributions Business Line 1 C ...

18 DETERMINATION OF THE CAPITAL CHARGE FOR OPERATIONAL RISK Table 1.7 Statistics from the aggregate loss distributions Business ...

YVES CRAMA, GEORGES HÜBNER AND JEAN-PHILIPPE PETERS 19 1,500,000 1,300,000 1,100,000 900,000 700,000 500,000 0,25 1 5 10 Collect ...

20 DETERMINATION OF THE CAPITAL CHARGE FOR OPERATIONAL RISK Consistentmeans that for largen, the estimates converge to the true ...

YVES CRAMA, GEORGES HÜBNER AND JEAN-PHILIPPE PETERS 21 de Fontnouvelle, P., Rosengren, E. and Jordan, J. (2004) “Implications of ...

CHAPTER 2 Incorporating Diversification into Risk Management Amiyatosh Purnanandam, Mitch Warachka, Yonggan Zhao and William T. ...

AMIYATOSH PURNANANDAM ET AL. 23 An entire literature on extensions of coherent risk measures followed ADEH. Rockafellar and Ziem ...

24 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT The organization of this chapter is as follows. Section 2.2 details the pr ...

AMIYATOSH PURNANANDAM ET AL. 25 to terminal portfolio values. Thus, the portfolio weights of the underlying assets cannot be alt ...

26 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT Define a trivial acceptable portfolioηcconsisting of $1 invested only in r ...

AMIYATOSH PURNANANDAM ET AL. 27 capableofofferingnegativecorrelation. Irrespectiveofthiscomplication, the dollar-denominated ris ...

28 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT Proposition2.2.2 Theproposedriskmeasurewithdiversificationhasthe following ...

AMIYATOSH PURNANANDAM ET AL. 29 2.2.2 Economic motivation An unacceptable portfolio may initially be chosen by a firm which beli ...

30 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT Overall, forη/∈Aη, diversification is beneficial from the firm’s perspecti ...

AMIYATOSH PURNANANDAM ET AL. 31 2.3 NUMERICAL EXAMPLE Consider an economy with two risky assets and riskfree capital. Uncertaint ...

32 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT Table 2.1 Asset payoffs at timeTin both scenarios Asset Heads Tails Riskfr ...

AMIYATOSH PURNANANDAM ET AL. 33 To clarify, portfolio theory selects portfolio weights to exploit diversifica- tionbeforechoosin ...

34 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT Altering equation (2.9) to minimize a function ofqT(η−η∗), whereqdenotes a ...

AMIYATOSH PURNANANDAM ET AL. 35 Theλparameters have interesting interpretations as each element cor- responds to a specific regu ...