Chunsheng Ban - Academia.edu (original) (raw)
Papers by Chunsheng Ban
Journal of Risk and Insurance, 2014
The recent financial crisis has posed new challenges to the pricing issue of mortgage insurance p... more The recent financial crisis has posed new challenges to the pricing issue of mortgage insurance premiums. By extending an option‐based approach to this pricing issue, we attempt to tackle several key challenges including the clustering of mortgage defaults, the diversification effect of underlying property pools, and mortgage insurers' information advantages. Our model partitions the volatility of collateralized property prices into idiosyncratic volatility and systematic volatility. Our results demonstrate that although the rising number of pooled mortgage loans can reduce the volatility of average default losses, the increasing correlation between the collateralized properties can lead to the volatility clustering of these losses.
SSRN Electronic Journal, 2012
The recent financial crisis has posed new challenges to the pricing issue of mortgage insurance p... more The recent financial crisis has posed new challenges to the pricing issue of mortgage insurance premiums. By extending an option-based approach to this pricing issue, we attempt to tackle several key challenges including the clustering of mortgage defaults, the diversification effect of underlying property pools and mortgage insurers' information advantages. Our model partitions the volatility of collateralized property prices into idiosyncratic volatility and systematic volatility. Our results demonstrate that although the rising number of pooled mortgage loans can reduce the volatility of average default losses, the increasing correlation between the collateralized properties can lead to the volatility clustering of these losses.
Proceedings of the American Mathematical Society, 1994
The auréole of an analytic germ ( X , x ) ⊂ ( C n , 0 ) (X,x) \subset ({\mathbb {C}^n},0) is a fi... more The auréole of an analytic germ ( X , x ) ⊂ ( C n , 0 ) (X,x) \subset ({\mathbb {C}^n},0) is a finite family of subcones of the reduced tangent cone | C X , x | |{C_{X,x}}| such that the set D X , x {D_{X,x}} of the limits of tangent hyperplanes to X X at x x is equal to ∪ ( Proj C α ) ∨ \cup {(\operatorname {Proj} \,{C_\alpha })^ \vee } . The auréole for a case of quasi-ordinary singularity is computed.
Proceedings of the American Mathematical Society, 1993
Let ( V , 0 ) ⊂ ( C d + 1 , 0 ) (V,0) \subset ({{\mathbf {C}}^{d + 1}},0) be a quasi-ordinary sin... more Let ( V , 0 ) ⊂ ( C d + 1 , 0 ) (V,0) \subset ({{\mathbf {C}}^{d + 1}},0) be a quasi-ordinary singularity and π : ( V , 0 ) → ( C d , 0 ) \pi :(V,0) \to ({{\mathbf {C}}^d},0) a quasi-ordinary projection. C d {{\mathbf {C}}^d} has a natural Whitney stratification given by the multiplicities of the discriminant locus of π \pi . It is proved that the pullback of this stratification gives a Whitney stratification of ( V , 0 ) (V,0) . Then using this result, an equisingular family of quasi-ordinary singularities is studied.
Abstract. We describe the embedded resolution of a quasi-ordinary surface singularity (V, p) whic... more Abstract. We describe the embedded resolution of a quasi-ordinary surface singularity (V, p) which results from applying the canonical resolution of Bierstone-Milman to (V, p). We show that this process depends solely on the characteristic pairs of (V, p), as predicted by Lipman. We describe the process explicitly enough that a resolution graph for f could in principle be obtained by computer using only the characteristic pairs. INTRODUCTION. The Jungian approach to resolving the singularities of an embedded surface V ⊂ C 3 begins with a projection π: V − → C 2 with (reduced) discriminant locus ∆ ⊂ C 2. Let σ: (M, σ −1 (∆)) − → (C 2, ∆) be an embedded resolution of the plane curve ∆. Thus, M is smooth (of dimension 2) and σ −1 (∆) has only normal crossings. The bimeromorphic map σ and the projection π induce
1.1. The goal of the present paper is the presentation of an “embedded resolution” of {f(x, y) + ... more 1.1. The goal of the present paper is the presentation of an “embedded resolution” of {f(x, y) + z 2 = 0}, 0) ⊂ (C 3, 0) using the method of Jung. In the first part of the introduction, we present the terminology and the strategy of the paper. Let (Y, 0) be the germ of an analytic space. We say that a proper, surjective
Contemporary Mathematics, 2000
... This is the only fact needed to prove [BMc] Theorem 2.5; the same argument works here. D Refe... more ... This is the only fact needed to prove [BMc] Theorem 2.5; the same argument works here. D References Bl. C. Ban, A Whitney stratification and equisingular family of quasi-ordinary singularities, Proc. Amer. Math. Soc. 117 (1993), 305-311. ...
Canadian Journal of Mathematics, 2002
We verify a generalization of (3.3) from [Lê73] proving that the homotopy type of the Milnor fibe... more We verify a generalization of (3.3) from [Lê73] proving that the homotopy type of the Milnor fiber of a reduced hypersurface singularity depends only on the embedded topological type of the singularity. In particular, using [Zariski68, Lipman83, Oh93, Gau88] for irreducible quasi-ordinary germs, it depends only on the normalized distinguished pairs of the singularity. The main result of the paper provides an explicit formula for the Euler-characteristic of the Milnor fiber in the surface case.
Canadian Journal of Mathematics, 2000
We describe the embedded resolution of a quasi-ordinary surface singularity (V, p) which results ... more We describe the embedded resolution of a quasi-ordinary surface singularity (V, p) which results from applying the canonical resolution of Bierstone-Milman to (V, p). We show that this process depends solely on the characteristic pairs of (V, p), as predicted by Lipman. We describe the process explicitly enough that a resolution graph for f could in principle be obtained by computer using only the characteristic pairs.
Studia Scientiarum Mathematicarum Hungarica, 2001
Journal of Risk and Insurance, 2014
The recent financial crisis has posed new challenges to the pricing issue of mortgage insurance p... more The recent financial crisis has posed new challenges to the pricing issue of mortgage insurance premiums. By extending an option‐based approach to this pricing issue, we attempt to tackle several key challenges including the clustering of mortgage defaults, the diversification effect of underlying property pools, and mortgage insurers' information advantages. Our model partitions the volatility of collateralized property prices into idiosyncratic volatility and systematic volatility. Our results demonstrate that although the rising number of pooled mortgage loans can reduce the volatility of average default losses, the increasing correlation between the collateralized properties can lead to the volatility clustering of these losses.
SSRN Electronic Journal, 2012
The recent financial crisis has posed new challenges to the pricing issue of mortgage insurance p... more The recent financial crisis has posed new challenges to the pricing issue of mortgage insurance premiums. By extending an option-based approach to this pricing issue, we attempt to tackle several key challenges including the clustering of mortgage defaults, the diversification effect of underlying property pools and mortgage insurers' information advantages. Our model partitions the volatility of collateralized property prices into idiosyncratic volatility and systematic volatility. Our results demonstrate that although the rising number of pooled mortgage loans can reduce the volatility of average default losses, the increasing correlation between the collateralized properties can lead to the volatility clustering of these losses.
Proceedings of the American Mathematical Society, 1994
The auréole of an analytic germ ( X , x ) ⊂ ( C n , 0 ) (X,x) \subset ({\mathbb {C}^n},0) is a fi... more The auréole of an analytic germ ( X , x ) ⊂ ( C n , 0 ) (X,x) \subset ({\mathbb {C}^n},0) is a finite family of subcones of the reduced tangent cone | C X , x | |{C_{X,x}}| such that the set D X , x {D_{X,x}} of the limits of tangent hyperplanes to X X at x x is equal to ∪ ( Proj C α ) ∨ \cup {(\operatorname {Proj} \,{C_\alpha })^ \vee } . The auréole for a case of quasi-ordinary singularity is computed.
Proceedings of the American Mathematical Society, 1993
Let ( V , 0 ) ⊂ ( C d + 1 , 0 ) (V,0) \subset ({{\mathbf {C}}^{d + 1}},0) be a quasi-ordinary sin... more Let ( V , 0 ) ⊂ ( C d + 1 , 0 ) (V,0) \subset ({{\mathbf {C}}^{d + 1}},0) be a quasi-ordinary singularity and π : ( V , 0 ) → ( C d , 0 ) \pi :(V,0) \to ({{\mathbf {C}}^d},0) a quasi-ordinary projection. C d {{\mathbf {C}}^d} has a natural Whitney stratification given by the multiplicities of the discriminant locus of π \pi . It is proved that the pullback of this stratification gives a Whitney stratification of ( V , 0 ) (V,0) . Then using this result, an equisingular family of quasi-ordinary singularities is studied.
Abstract. We describe the embedded resolution of a quasi-ordinary surface singularity (V, p) whic... more Abstract. We describe the embedded resolution of a quasi-ordinary surface singularity (V, p) which results from applying the canonical resolution of Bierstone-Milman to (V, p). We show that this process depends solely on the characteristic pairs of (V, p), as predicted by Lipman. We describe the process explicitly enough that a resolution graph for f could in principle be obtained by computer using only the characteristic pairs. INTRODUCTION. The Jungian approach to resolving the singularities of an embedded surface V ⊂ C 3 begins with a projection π: V − → C 2 with (reduced) discriminant locus ∆ ⊂ C 2. Let σ: (M, σ −1 (∆)) − → (C 2, ∆) be an embedded resolution of the plane curve ∆. Thus, M is smooth (of dimension 2) and σ −1 (∆) has only normal crossings. The bimeromorphic map σ and the projection π induce
1.1. The goal of the present paper is the presentation of an “embedded resolution” of {f(x, y) + ... more 1.1. The goal of the present paper is the presentation of an “embedded resolution” of {f(x, y) + z 2 = 0}, 0) ⊂ (C 3, 0) using the method of Jung. In the first part of the introduction, we present the terminology and the strategy of the paper. Let (Y, 0) be the germ of an analytic space. We say that a proper, surjective
Contemporary Mathematics, 2000
... This is the only fact needed to prove [BMc] Theorem 2.5; the same argument works here. D Refe... more ... This is the only fact needed to prove [BMc] Theorem 2.5; the same argument works here. D References Bl. C. Ban, A Whitney stratification and equisingular family of quasi-ordinary singularities, Proc. Amer. Math. Soc. 117 (1993), 305-311. ...
Canadian Journal of Mathematics, 2002
We verify a generalization of (3.3) from [Lê73] proving that the homotopy type of the Milnor fibe... more We verify a generalization of (3.3) from [Lê73] proving that the homotopy type of the Milnor fiber of a reduced hypersurface singularity depends only on the embedded topological type of the singularity. In particular, using [Zariski68, Lipman83, Oh93, Gau88] for irreducible quasi-ordinary germs, it depends only on the normalized distinguished pairs of the singularity. The main result of the paper provides an explicit formula for the Euler-characteristic of the Milnor fiber in the surface case.
Canadian Journal of Mathematics, 2000
We describe the embedded resolution of a quasi-ordinary surface singularity (V, p) which results ... more We describe the embedded resolution of a quasi-ordinary surface singularity (V, p) which results from applying the canonical resolution of Bierstone-Milman to (V, p). We show that this process depends solely on the characteristic pairs of (V, p), as predicted by Lipman. We describe the process explicitly enough that a resolution graph for f could in principle be obtained by computer using only the characteristic pairs.
Studia Scientiarum Mathematicarum Hungarica, 2001