I think you should fix value when getting date value to return Date | null:
class DatePicker extends kendo.ui.Widget { static fn: DatePicker; options: DatePickerOptions; element: JQuery; wrapper: JQuery; static extend(proto: Object): DatePicker; constructor(element: Element, options?: DatePickerOptions); close(): void; destroy(): void; enable(enable: boolean): void; readonly(readonly: boolean): void; max(): Date; max(value: Date): void; max(value: string): void; min(): Date; min(value: Date): void; min(value: string): void; open(): void; setOptions(options: any): void; value(): Date; //!!! OR null value(value: Date): void; value(value: string): void;}